diff --git a/ocaml/driver/compile_common.ml b/ocaml/driver/compile_common.ml
index babf71d24ae..8b115ceb4f6 100644
--- a/ocaml/driver/compile_common.ml
+++ b/ocaml/driver/compile_common.ml
@@ -64,9 +64,7 @@ let typecheck_intf info ast =
   let tsg =
     ast
     |> Typemod.type_interface
-        ~sourcefile:info.source_file
-        info.module_name
-        info.env
+         ~sourcefile:info.source_file info.module_name info.env
     |> print_if info.ppf_dump Clflags.dump_typedtree Printtyped.interface
   in
   let sg = tsg.Typedtree.sig_type in
@@ -87,8 +85,14 @@ let emit_signature info ast tsg =
     let kind : Cmi_format.kind =
       if !Clflags.as_parameter then
         Parameter
-      else
-        Normal { cmi_impl = info.module_name }
+      else begin
+        let cmi_arg_for =
+          match !Clflags.as_argument_for with
+          | Some arg_type -> Some (Compilation_unit.Name.of_string arg_type)
+          | None -> None
+        in
+        Normal { cmi_impl = info.module_name; cmi_arg_for }
+      end
     in
     let alerts = Builtin_attributes.alerts_of_sig ast in
     Env.save_signature ~alerts tsg.Typedtree.sig_type
diff --git a/ocaml/driver/main_args.ml b/ocaml/driver/main_args.ml
index 2a91eb631e8..434cc33b63a 100644
--- a/ocaml/driver/main_args.ml
+++ b/ocaml/driver/main_args.ml
@@ -659,6 +659,11 @@ let mk_as_parameter f =
   " Compiles the interface as a parameter for an open module."
 ;;
 
+let mk_as_argument_for f =
+  "-as-argument-for", Arg.String f,
+  "<module name> Compiles the module as an argument for the named parameter."
+;;
+
 let mk_use_prims f =
   "-use-prims", Arg.String f, "<file>  (undocumented)"
 
@@ -965,6 +970,7 @@ end
 module type Compiler_options = sig
   val _a : unit -> unit
   val _annot : unit -> unit
+  val _as_argument_for : string -> unit
   val _as_parameter : unit -> unit
   val _binannot : unit -> unit
   val _binannot_cms : unit -> unit
@@ -1165,6 +1171,7 @@ struct
     mk_absname F._absname;
     mk_no_absname F._no_absname;
     mk_annot F._annot;
+    mk_as_argument_for F._as_argument_for;
     mk_as_parameter F._as_parameter;
     mk_binannot F._binannot;
     mk_binannot_cms F._binannot_cms;
@@ -1383,6 +1390,7 @@ struct
     mk_afl_instrument F._afl_instrument;
     mk_afl_inst_ratio F._afl_inst_ratio;
     mk_annot F._annot;
+    mk_as_argument_for F._as_argument_for;
     mk_as_parameter F._as_parameter;
     mk_binannot F._binannot;
     mk_binannot_cms F._binannot_cms;
@@ -1970,6 +1978,7 @@ module Default = struct
     let _annot = set annotations
     let _args = Arg.read_arg
     let _args0 = Arg.read_arg0
+    let _as_argument_for s = as_argument_for := Some s
     let _as_parameter = set as_parameter
     let _binannot = set binary_annotations
     let _binannot_cms = set binary_annotations_cms
diff --git a/ocaml/driver/main_args.mli b/ocaml/driver/main_args.mli
index dfb2797bb7a..7e136ed0abc 100644
--- a/ocaml/driver/main_args.mli
+++ b/ocaml/driver/main_args.mli
@@ -88,6 +88,7 @@ end
 module type Compiler_options = sig
   val _a : unit -> unit
   val _annot : unit -> unit
+  val _as_argument_for : string -> unit
   val _as_parameter : unit -> unit
   val _binannot : unit -> unit
   val _binannot_cms : unit -> unit
diff --git a/ocaml/file_formats/cmi_format.ml b/ocaml/file_formats/cmi_format.ml
index 1e0b86aa173..c32599d0024 100644
--- a/ocaml/file_formats/cmi_format.ml
+++ b/ocaml/file_formats/cmi_format.ml
@@ -23,6 +23,7 @@ type pers_flags =
 type kind =
   | Normal of {
       cmi_impl : Compilation_unit.t;
+      cmi_arg_for : Compilation_unit.Name.t option;
     }
   | Parameter
 
diff --git a/ocaml/file_formats/cmi_format.mli b/ocaml/file_formats/cmi_format.mli
index 72fef143c25..d80e47863fe 100644
--- a/ocaml/file_formats/cmi_format.mli
+++ b/ocaml/file_formats/cmi_format.mli
@@ -23,6 +23,7 @@ type pers_flags =
 type kind =
   | Normal of {
       cmi_impl : Compilation_unit.t;
+      cmi_arg_for : Compilation_unit.Name.t option;
     }
   | Parameter
 
diff --git a/ocaml/ocamldoc/odoc_analyse.ml b/ocaml/ocamldoc/odoc_analyse.ml
index 83845098fb4..82d92ab0267 100644
--- a/ocaml/ocamldoc/odoc_analyse.ml
+++ b/ocaml/ocamldoc/odoc_analyse.ml
@@ -122,7 +122,9 @@ let process_interface_file sourcefile =
     Pparse.file ~tool_name inputfile
       (no_docstring Parse.interface) Pparse.Signature
   in
-  let sg = Typemod.type_interface ~sourcefile compilation_unit (initial_env()) ast in
+  let sg =
+    Typemod.type_interface ~sourcefile compilation_unit (initial_env()) ast
+  in
   Warnings.check_fatal ();
   (ast, sg, inputfile)
 
diff --git a/ocaml/testsuite/tests/templates/basic/bad_arg_impl.ml b/ocaml/testsuite/tests/templates/basic/bad_arg_impl.ml
new file mode 100644
index 00000000000..86371fc4034
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/bad_arg_impl.ml
@@ -0,0 +1,4 @@
+type t = unit
+
+let empty = ()
+let append () () = `Banana
diff --git a/ocaml/testsuite/tests/templates/basic/bad_arg_impl.reference b/ocaml/testsuite/tests/templates/basic/bad_arg_impl.reference
new file mode 100644
index 00000000000..128ba2632bd
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/bad_arg_impl.reference
@@ -0,0 +1,12 @@
+File "bad_arg_impl.ml", line 1:
+Error: The argument module bad_arg_impl.ml
+       does not match the parameter signature monoid.cmi: 
+       Values do not match:
+         val append : unit -> unit -> [> `Banana ]
+       is not included in
+         val append : t -> t -> t
+       The type unit -> unit -> [> `Banana ] is not compatible with the type
+         t -> t -> t
+       Type [> `Banana ] is not compatible with type t = unit
+       File "monoid.mli", line 4, characters 0-24: Expected declaration
+       File "bad_arg_impl.ml", line 4, characters 4-10: Actual declaration
diff --git a/ocaml/testsuite/tests/templates/basic/bad_arg_intf.mli b/ocaml/testsuite/tests/templates/basic/bad_arg_intf.mli
new file mode 100644
index 00000000000..13c9b7ff4ab
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/bad_arg_intf.mli
@@ -0,0 +1,4 @@
+type t
+
+val empty : t
+val append : t -> t -> [ `Banana ]
diff --git a/ocaml/testsuite/tests/templates/basic/bad_arg_intf.reference b/ocaml/testsuite/tests/templates/basic/bad_arg_intf.reference
new file mode 100644
index 00000000000..2c5c65e3503
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/bad_arg_intf.reference
@@ -0,0 +1,12 @@
+File "bad_arg_intf.mli", line 1:
+Error: The argument module bad_arg_intf.mli
+       does not match the parameter signature monoid.cmi: 
+       Values do not match:
+         val append : t -> t -> [ `Banana ]
+       is not included in
+         val append : t -> t -> t
+       The type t -> t -> [ `Banana ] is not compatible with the type
+         t -> t -> t
+       Type [ `Banana ] is not compatible with type t
+       File "monoid.mli", line 4, characters 0-24: Expected declaration
+       File "bad_arg_intf.mli", line 4, characters 0-34: Actual declaration
diff --git a/ocaml/testsuite/tests/templates/basic/string_monoid.ml b/ocaml/testsuite/tests/templates/basic/string_monoid.ml
new file mode 100644
index 00000000000..43385c451b3
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/string_monoid.ml
@@ -0,0 +1,4 @@
+type t = string
+
+let empty = ""
+let append = (^)
diff --git a/ocaml/testsuite/tests/templates/basic/string_monoid.mli b/ocaml/testsuite/tests/templates/basic/string_monoid.mli
new file mode 100644
index 00000000000..a915a865726
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/string_monoid.mli
@@ -0,0 +1,4 @@
+type t = string
+
+val empty : t
+val append : t -> t -> t
diff --git a/ocaml/testsuite/tests/templates/basic/test.ml b/ocaml/testsuite/tests/templates/basic/test.ml
index d6ed4eddc58..0b50f8f3775 100644
--- a/ocaml/testsuite/tests/templates/basic/test.ml
+++ b/ocaml/testsuite/tests/templates/basic/test.ml
@@ -1,13 +1,136 @@
 (* TEST
- readonly_files = "bad_ref_direct.ml bad_ref_direct.reference monoid.mli ";
- setup-ocamlc.byte-build-env;
- flags = "-as-parameter";
- module = "monoid.mli";
- ocamlc.byte;
- module = "bad_ref_direct.ml";
- compiler_output = "bad_ref_direct.output";
- ocamlc_byte_exit_status = "2";
- ocamlc.byte;
- compiler_reference = "bad_ref_direct.reference";
- check-ocamlc.byte-output;
+ readonly_files = "\
+   bad_arg_impl.ml bad_arg_impl.reference \
+   bad_arg_intf.mli bad_arg_intf.reference \
+   bad_ref_direct.ml bad_ref_direct.reference \
+   monoid.mli \
+   string_monoid.ml string_monoid.mli \
+   test_direct_access.ml test_direct_access.reference \
+ ";
+
+ {
+   setup-ocamlc.byte-build-env;
+
+   flags = "-as-parameter";
+   module = "monoid.mli";
+   ocamlc.byte;
+   {
+     flags = "";
+     module = "bad_ref_direct.ml";
+     compiler_output = "bad_ref_direct.output";
+     ocamlc_byte_exit_status = "2";
+     ocamlc.byte;
+
+     compiler_reference = "bad_ref_direct.reference";
+     check-ocamlc.byte-output;
+   }{
+     flags = "-as-argument-for Monoid";
+     module = "bad_arg_impl.ml";
+     compiler_output = "bad_arg_impl.output";
+     ocamlc_byte_exit_status = "2";
+     ocamlc.byte;
+
+     compiler_reference = "bad_arg_impl.reference";
+     check-ocamlc.byte-output;
+   }{
+     flags = "-as-argument-for Monoid";
+     module = "bad_arg_intf.mli";
+     compiler_output = "bad_arg_intf.output";
+     ocamlc_byte_exit_status = "2";
+     ocamlc.byte;
+
+     compiler_reference = "bad_arg_intf.reference";
+     check-ocamlc.byte-output;
+   }{
+     src = "string_monoid.ml";
+     dst = "string_monoid_no_mli.ml";
+     copy;
+
+     flags = "-as-argument-for Monoid";
+     module = "string_monoid_no_mli.ml string_monoid.mli string_monoid.ml";
+     ocamlc.byte;
+
+     flags = "";
+     module = "test_direct_access.ml";
+     ocamlc.byte;
+
+     flags = "";
+     program = "${test_build_directory}/test_direct_access.bc";
+     module = "";
+     all_modules = "\
+       string_monoid.cmo \
+       string_monoid_no_mli.cmo \
+       test_direct_access.cmo \
+     ";
+     ocamlc.byte;
+
+     output = "test_direct_access.output";
+     run;
+
+     reference = "test_direct_access.reference";
+     check-program-output;
+   }
+ }{
+   setup-ocamlopt.byte-build-env;
+
+   flags = "-as-parameter";
+   module = "monoid.mli";
+   ocamlopt.byte;
+   {
+     flags = "";
+     module = "bad_ref_direct.ml";
+     compiler_output = "bad_ref_direct.output";
+     ocamlopt_byte_exit_status = "2";
+     ocamlopt.byte;
+
+     compiler_reference = "bad_ref_direct.reference";
+     check-ocamlopt.byte-output;
+   }{
+     flags = "-as-argument-for Monoid";
+     module = "bad_arg_impl.ml";
+     compiler_output = "bad_arg_impl.output";
+     ocamlopt_byte_exit_status = "2";
+     ocamlopt.byte;
+
+     compiler_reference = "bad_arg_impl.reference";
+     check-ocamlopt.byte-output;
+   }{
+     flags = "-as-argument-for Monoid";
+     module = "bad_arg_intf.mli";
+     compiler_output = "bad_arg_intf.output";
+     ocamlopt_byte_exit_status = "2";
+     ocamlopt.byte;
+
+     compiler_reference = "bad_arg_intf.reference";
+     check-ocamlopt.byte-output;
+   }{
+     src = "string_monoid.ml";
+     dst = "string_monoid_no_mli.ml";
+     copy;
+
+     flags = "-as-argument-for Monoid";
+     module = "string_monoid_no_mli.ml string_monoid.mli string_monoid.ml";
+     ocamlopt.byte;
+
+     flags = "";
+     module = "test_direct_access.ml";
+     ocamlopt.byte;
+
+     flags = "";
+     program = "${test_build_directory}/test_direct_access.exe";
+     module = "";
+     all_modules = "\
+       string_monoid.cmx \
+       string_monoid_no_mli.cmx \
+       test_direct_access.cmx \
+     ";
+     ocamlopt.byte;
+
+     output = "test_direct_access.output";
+     run;
+
+     reference = "test_direct_access.reference";
+     check-program-output;
+   }
+ }
 *)
diff --git a/ocaml/testsuite/tests/templates/basic/test_direct_access.ml b/ocaml/testsuite/tests/templates/basic/test_direct_access.ml
new file mode 100644
index 00000000000..01cb6358343
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/test_direct_access.ml
@@ -0,0 +1,5 @@
+let () =
+  let open Printf in
+  printf "With .mli: %s\n" (String_monoid.append "Hello " "world!");
+  printf "Without .mli: %s\n" (String_monoid_no_mli.append "Hello " "world!");
+  ()
diff --git a/ocaml/testsuite/tests/templates/basic/test_direct_access.reference b/ocaml/testsuite/tests/templates/basic/test_direct_access.reference
new file mode 100644
index 00000000000..bd0888b5798
--- /dev/null
+++ b/ocaml/testsuite/tests/templates/basic/test_direct_access.reference
@@ -0,0 +1,2 @@
+With .mli: Hello world!
+Without .mli: Hello world!
diff --git a/ocaml/typing/env.ml b/ocaml/typing/env.ml
index c5cc6dec877..6c4e7e77189 100644
--- a/ocaml/typing/env.ml
+++ b/ocaml/typing/env.ml
@@ -1015,7 +1015,10 @@ let register_import_as_opaque modname =
   Persistent_env.register_import_as_opaque !persistent_env modname
 
 let is_parameter_unit modname =
-  Persistent_env.is_registered_parameter_import !persistent_env modname
+  Persistent_env.is_parameter_import !persistent_env modname
+
+let implemented_parameter modname =
+  Persistent_env.implemented_parameter !persistent_env modname
 
 let reset_declaration_caches () =
   Types.Uid.Tbl.clear !value_declarations;
@@ -2639,6 +2642,9 @@ let read_signature modname filename ~add_binding =
   let mty = read_pers_mod modname filename ~add_binding in
   Subst.Lazy.force_signature mty
 
+let register_parameter_import import =
+  Persistent_env.register_parameter_import !persistent_env import
+
 let is_identchar_latin1 = function
   | 'A'..'Z' | 'a'..'z' | '_' | '\192'..'\214' | '\216'..'\246'
   | '\248'..'\255' | '\'' | '0'..'9' -> true
diff --git a/ocaml/typing/env.mli b/ocaml/typing/env.mli
index 1e1cfa42561..0f4a598a57e 100644
--- a/ocaml/typing/env.mli
+++ b/ocaml/typing/env.mli
@@ -477,6 +477,9 @@ val save_signature_with_imports:
         (* Arguments: signature, module name, module kind,
            file name, imported units with their CRCs. *)
 
+(* Register a module as a parameter to this unit. *)
+val register_parameter_import: Compilation_unit.Name.t -> unit
+
 (* Return the CRC of the interface of the given compilation unit *)
 val crc_of_unit: Compilation_unit.Name.t -> Digest.t
 
@@ -496,6 +499,11 @@ val register_import_as_opaque: Compilation_unit.Name.t -> unit
    -as-parameter *)
 val is_parameter_unit: Compilation_unit.Name.t -> bool
 
+(* [implemented_parameter md] is the argument given to -as-argument-for when
+   [md] was compiled *)
+val implemented_parameter:
+  Compilation_unit.Name.t -> Compilation_unit.Name.t option
+
 (* Summaries -- compact representation of an environment, to be
    exported in debugging information. *)
 
diff --git a/ocaml/typing/includemod.ml b/ocaml/typing/includemod.ml
index 85d3e199139..8bf373bf204 100644
--- a/ocaml/typing/includemod.ml
+++ b/ocaml/typing/includemod.ml
@@ -100,8 +100,13 @@ module Error = struct
         {less_than:module_type_diff; greater_than: module_type_diff}
 
 
+  type compilation_unit_comparison =
+    | Implementation_vs_interface
+    | Argument_vs_parameter
+
   type all =
-    | In_Compilation_unit of (string, signature_symptom) diff
+    | In_Compilation_unit of
+        compilation_unit_comparison * (string, signature_symptom) diff
     | In_Signature of signature_symptom
     | In_Include_functor_signature of signature_symptom
     | In_Module_type of module_type_diff
@@ -1056,16 +1061,30 @@ let () =
 (* Check that an implementation of a compilation unit meets its
    interface. *)
 
-let compunit env ~mark impl_name impl_sig intf_name intf_sig unit_shape =
+let compunit0
+    ~comparison env ~mark impl_name impl_sig intf_name intf_sig unit_shape =
   match
     signatures ~in_eq:false ~loc:(Location.in_file impl_name) env ~mark
       Subst.identity impl_sig intf_sig unit_shape
   with Result.Error reasons ->
+    let diff = Error.diff impl_name intf_name reasons in
     let cdiff =
-      Error.In_Compilation_unit(Error.diff impl_name intf_name reasons) in
+      Error.In_Compilation_unit(comparison, diff) in
     raise(Error(env, cdiff))
   | Ok x -> x
 
+let compunit = compunit0 ~comparison:Implementation_vs_interface
+
+(* Check that the interface of a compilation unit meets the interface of the
+   parameter it's declared to be an argument for using [-as-argument-for] *)
+
+let compunit_as_argument env arg_name arg_sig param_name param_sig =
+  let cc, _shape =
+    compunit0 env arg_name arg_sig param_name param_sig Shape.dummy_mod
+      ~comparison:Argument_vs_parameter ~mark:Mark_positive
+  in
+  cc
+
 (* Functor diffing computation:
    The diffing computation uses the internal typing function
  *)
diff --git a/ocaml/typing/includemod.mli b/ocaml/typing/includemod.mli
index e96c39dd18d..6cb215cc6d5 100644
--- a/ocaml/typing/includemod.mli
+++ b/ocaml/typing/includemod.mli
@@ -109,9 +109,13 @@ module Error: sig
     | Incomparable of
         {less_than:module_type_diff; greater_than: module_type_diff}
 
+  type compilation_unit_comparison =
+    | Implementation_vs_interface
+    | Argument_vs_parameter
 
   type all =
-    | In_Compilation_unit of (string, signature_symptom) diff
+    | In_Compilation_unit of
+        compilation_unit_comparison * (string, signature_symptom) diff
     | In_Signature of signature_symptom
     | In_Include_functor_signature of signature_symptom
     | In_Module_type of module_type_diff
@@ -181,6 +185,9 @@ val compunit:
       Env.t -> mark:mark -> string -> signature ->
       string -> signature -> Shape.t -> module_coercion * Shape.t
 
+val compunit_as_argument:
+      Env.t -> string -> signature -> string -> signature -> module_coercion
+
 val type_declarations:
   loc:Location.t -> Env.t -> mark:mark ->
   Ident.t -> type_declaration -> type_declaration -> unit
diff --git a/ocaml/typing/includemod_errorprinter.ml b/ocaml/typing/includemod_errorprinter.ml
index be5cc0be2ca..44994492cd7 100644
--- a/ocaml/typing/includemod_errorprinter.ml
+++ b/ocaml/typing/includemod_errorprinter.ml
@@ -710,6 +710,16 @@ let interface_mismatch ppf (diff: _ Err.diff) =
     "The implementation %s@ does not match the interface %s:@ "
     diff.got diff.expected
 
+let parameter_mismatch ppf (diff: _ Err.diff) =
+  Format.fprintf ppf
+    "The argument module %s@ does not match the parameter signature %s:@ "
+    diff.got diff.expected
+
+let compilation_unit_mismatch comparison ppf diff =
+  match (comparison : Err.compilation_unit_comparison) with
+  | Implementation_vs_interface -> interface_mismatch ppf diff
+  | Argument_vs_parameter -> parameter_mismatch ppf diff
+
 let core_module_type_symptom (x:Err.core_module_type_symptom)  =
   match x with
   | Not_an_alias | Not_an_identifier | Abstract_module_type
@@ -886,8 +896,10 @@ let module_type_subst ~env id diff =
       [main]
 
 let all env = function
-  | In_Compilation_unit diff ->
-      let first = Location.msg "%a" interface_mismatch diff in
+  | In_Compilation_unit (comparison, diff) ->
+      let first =
+        Location.msg "%a" (compilation_unit_mismatch comparison) diff
+      in
       signature ~expansion_token:true ~env ~before:[first] ~ctx:[] diff.symptom
   | In_Type_declaration (id,reason) ->
       [Location.msg "%t" (core env id reason)]
diff --git a/ocaml/typing/persistent_env.ml b/ocaml/typing/persistent_env.ml
index 68e48dc6856..2729eaeb3e1 100644
--- a/ocaml/typing/persistent_env.ml
+++ b/ocaml/typing/persistent_env.ml
@@ -35,7 +35,6 @@ type error =
       CU.t * filepath * CU.Prefix.t
   | Illegal_import_of_parameter of CU.Name.t * filepath
   | Not_compiled_as_parameter of CU.Name.t * filepath
-  | Cannot_implement_parameter of CU.Name.t * filepath
 
 exception Error of error
 let error err = raise (Error err)
@@ -64,6 +63,7 @@ type can_load_cmis =
 (* Data relating directly to a .cmi *)
 type import = {
   imp_is_param : bool;
+  imp_arg_for : Compilation_unit.Name.t option;
   imp_impl : CU.t option;
   imp_sign : Subst.Lazy.signature;
   imp_filename : string;
@@ -200,6 +200,11 @@ let check_consistency penv imp =
 let is_registered_parameter_import {param_imports; _} import =
   CU.Name.Set.mem import !param_imports
 
+let is_parameter_import t import =
+  match find_import_info_in_cache t import with
+  | Some { imp_is_param; _ } -> imp_is_param
+  | None -> Misc.fatal_errorf "is_parameter_import %a" CU.Name.print import
+
 let can_load_cmis penv =
   !(penv.can_load_cmis)
 let set_can_load_cmis penv setting =
@@ -232,6 +237,9 @@ let save_import penv crc modname impl flags filename =
   Consistbl.check crc_units modname impl crc filename;
   add_import penv modname
 
+(* Add an import to the hash table. Checks that we are allowed to access
+   this .cmi. *)
+
 let acknowledge_import penv ~check modname pers_sig =
   let { Persistent_signature.filename; cmi; visibility } = pers_sig in
   let found_name = cmi.cmi_name in
@@ -267,31 +275,15 @@ let acknowledge_import penv ~check modname pers_sig =
     | Normal _ -> false
     | Parameter -> true
   in
-  (* CR-someday lmaurer: Consider moving this check into
-     [acknowledge_pers_struct]. It makes more sense to flag these errors when
-     the identifier is in source, rather than, say, a signature we're reading
-     from a file, especially if it's our own .mli. *)
-  begin match is_param, is_registered_parameter_import penv modname with
-  | true, false ->
-      begin match CU.get_current () with
-      | Some current_unit when CU.Name.equal modname (CU.name current_unit) ->
-          error (Cannot_implement_parameter (modname, filename))
-      | _ ->
-          error (Illegal_import_of_parameter(modname, filename))
-      end
-  | false, true ->
-      error (Not_compiled_as_parameter(modname, filename))
-  | true, true
-  | false, false -> ()
-  end;
-  let impl =
+  let arg_for, impl =
     match kind with
-    | Normal { cmi_impl } -> Some cmi_impl
-    | Parameter -> None
+    | Normal { cmi_arg_for; cmi_impl } -> cmi_arg_for, Some cmi_impl
+    | Parameter -> None, None
   in
   let {imports; _} = penv in
   let import =
     { imp_is_param = is_param;
+      imp_arg_for = arg_for;
       imp_impl = impl;
       imp_sign = sign;
       imp_filename = filename;
@@ -356,11 +348,24 @@ type 'a sig_reader =
   -> flags:Cmi_format.pers_flags list
   -> 'a
 
+(* Add a persistent structure to the hash table and bind it in the [Env].
+   Checks that OCaml source is allowed to refer to this module. *)
+
 let acknowledge_pers_struct penv modname import val_of_pers_sig =
   let {persistent_structures; _} = penv in
+  let is_param = import.imp_is_param in
   let impl = import.imp_impl in
   let sign = import.imp_sign in
+  let filename = import.imp_filename in
   let flags = import.imp_flags in
+  begin match is_param, is_registered_parameter_import penv modname with
+  | true, false ->
+      error (Illegal_import_of_parameter(modname, filename))
+  | false, true ->
+      error (Not_compiled_as_parameter(modname, filename))
+  | true, true
+  | false, false -> ()
+  end;
   let binding = make_binding penv impl in
   let address : address =
     match binding with
@@ -440,7 +445,6 @@ let check_pers_struct ~allow_hidden penv f ~loc name =
               describe_prefix prefix
         | Illegal_import_of_parameter _ -> assert false
         | Not_compiled_as_parameter _ -> assert false
-        | Cannot_implement_parameter _ -> assert false
       in
       let warn = Warnings.No_cmi_file(name_as_string, Some msg) in
         Location.prerr_warning loc warn
@@ -509,6 +513,11 @@ let is_imported {imported_units; _} s =
 let is_imported_opaque {imported_opaque_units; _} s =
   CU.Name.Set.mem s !imported_opaque_units
 
+let implemented_parameter penv modname =
+  match find_import_info_in_cache penv modname with
+  | Some { imp_arg_for; _ } -> imp_arg_for
+  | None -> None
+
 let make_cmi penv modname kind sign alerts =
   let flags =
     List.concat [
@@ -596,11 +605,6 @@ let report_error ppf =
         filename
         describe_prefix prefix
         "Can only access members of this library's package or a containing package"
-  | Cannot_implement_parameter(modname, _filename) ->
-      fprintf ppf
-        "@[<hov>The interface for %a@ was compiled with -as-parameter.@ \
-         It cannot be implemented directly.@]"
-        CU.Name.print modname
 
 let () =
   Location.register_error_of_exn
diff --git a/ocaml/typing/persistent_env.mli b/ocaml/typing/persistent_env.mli
index 765d7a23e21..32d4086eb7e 100644
--- a/ocaml/typing/persistent_env.mli
+++ b/ocaml/typing/persistent_env.mli
@@ -34,7 +34,6 @@ type error =
       Compilation_unit.t * filepath * Compilation_unit.Prefix.t
   | Illegal_import_of_parameter of Compilation_unit.Name.t * filepath
   | Not_compiled_as_parameter of Compilation_unit.Name.t * filepath
-  | Cannot_implement_parameter of Compilation_unit.Name.t * filepath
 
 
 exception Error of error
@@ -84,6 +83,8 @@ type 'a sig_reader =
 
 (* If [add_binding] is false, reads the signature from the .cmi but does not
    bind the module name in the environment. *)
+(* CR-someday lmaurer: [add_binding] is apparently always false, including in the
+   [-instantiate] branch. We should remove this parameter. *)
 val read : 'a t -> 'a sig_reader
   -> Compilation_unit.Name.t -> filepath -> add_binding:bool -> Subst.Lazy.signature
 val find : allow_hidden:bool -> 'a t -> 'a sig_reader
@@ -94,15 +95,14 @@ val find_in_cache : 'a t -> Compilation_unit.Name.t -> 'a option
 val check : allow_hidden:bool -> 'a t -> 'a sig_reader
   -> loc:Location.t -> Compilation_unit.Name.t -> unit
 
-(* Lets it be known that the given module is a parameter and thus is expected
-   to have been compiled as such. It may or may not be a parameter to _this_
-   module (see the forthcoming [register_exported_parameter]). Raises an
-   exception if the module has already been imported as a non-parameter. *)
+(* Lets it be known that the given module is a parameter to this module and thus is
+   expected to have been compiled as such. Raises an exception if the module has already
+   been imported as a non-parameter. *)
 val register_parameter_import : 'a t -> Compilation_unit.Name.t -> unit
 
-(* [is_registered_parameter_import penv md] checks if [md] has been passed to
-   [register_parameter_import penv] *)
-val is_registered_parameter_import : 'a t -> Compilation_unit.Name.t -> bool
+(* [is_parameter_import penv md] checks if [md] is a parameter. Raises a fatal
+   error if the module has not been imported. *)
+val is_parameter_import : 'a t -> Compilation_unit.Name.t -> bool
 
 (* [looked_up penv md] checks if one has already tried
    to read the signature for [md] in the environment
@@ -121,6 +121,11 @@ val is_imported_opaque : 'a t -> Compilation_unit.Name.t -> bool
    opaque module *)
 val register_import_as_opaque : 'a t -> Compilation_unit.Name.t -> unit
 
+(* [implemented_parameter penv md] returns the argument to [-as-argument-for]
+   that [md] was compiled with. *)
+val implemented_parameter : 'a t -> Compilation_unit.Name.t
+  -> Compilation_unit.Name.t option
+
 val make_cmi : 'a t
   -> Compilation_unit.Name.t
   -> Cmi_format.kind
diff --git a/ocaml/typing/typedtree.ml b/ocaml/typing/typedtree.ml
index ff8bc5131d9..6ad7b86e9d5 100644
--- a/ocaml/typing/typedtree.ml
+++ b/ocaml/typing/typedtree.ml
@@ -798,10 +798,16 @@ and 'a class_infos =
     ci_attributes: attribute list;
    }
 
+type argument_interface = {
+  ai_signature: Types.signature;
+  ai_coercion_from_primary: module_coercion;
+}
+
 type implementation = {
   structure: structure;
   coercion: module_coercion;
   signature: Types.signature;
+  argument_interface: argument_interface option;
   shape: Shape.t;
 }
 
diff --git a/ocaml/typing/typedtree.mli b/ocaml/typing/typedtree.mli
index bdd199496e1..f1fbb19f10d 100644
--- a/ocaml/typing/typedtree.mli
+++ b/ocaml/typing/typedtree.mli
@@ -1056,10 +1056,20 @@ and 'a class_infos =
     ci_attributes: attributes;
    }
 
+type argument_interface = {
+  ai_signature: Types.signature;
+  ai_coercion_from_primary: module_coercion;
+}
+(** For a module [M] compiled with [-as-argument-for P] for some parameter
+    module [P], the signature of [P] along with the coercion from [M]'s
+    exported signature (the _primary interface_) to [P]'s signature (the
+    _argument interface_). *)
+
 type implementation = {
   structure: structure;
   coercion: module_coercion;
   signature: Types.signature;
+  argument_interface: argument_interface option;
   shape: Shape.t;
 }
 (** A typechecked implementation including its module structure, its exported
@@ -1070,6 +1080,10 @@ type implementation = {
 
     If there isn't one, the signature will be inferred from the module
     structure.
+
+    If the module is compiled with [-as-argument-for] and is thus typechecked
+    against the .mli for a parameter in addition to its own .mli, it has an
+    additional signature stored in [argument_interface].
 *)
 
 type item_declaration =
diff --git a/ocaml/typing/typemod.ml b/ocaml/typing/typemod.ml
index b1fbf9bd977..d3ca2059580 100644
--- a/ocaml/typing/typemod.ml
+++ b/ocaml/typing/typemod.ml
@@ -90,6 +90,14 @@ type error =
   | Strengthening_mismatch of Longident.t * Includemod.explanation
   | Cannot_pack_parameter
   | Cannot_compile_implementation_as_parameter
+  | Cannot_implement_parameter of Compilation_unit.Name.t * Misc.filepath
+  | Argument_for_non_parameter of Compilation_unit.Name.t * Misc.filepath
+  | Cannot_find_argument_type of Compilation_unit.Name.t
+  | Inconsistent_argument_types of {
+      new_arg_type : Compilation_unit.Name.t option;
+      old_arg_type : Compilation_unit.Name.t option;
+      old_source_file : Misc.filepath;
+    }
 
 exception Error of Location.t * Env.t * error
 exception Error_forward of Location.error
@@ -3375,6 +3383,36 @@ let cms_register_toplevel_struct_attributes ~sourcefile ~uid ast =
         | { pstr_desc = Pstr_attribute attr; _ }  -> Some attr
         | _ -> None)
 
+let check_argument_type_if_given env sourcefile actual_sig arg_module_opt =
+  match arg_module_opt with
+  | None -> None
+  | Some arg_module ->
+      let arg_import =
+        (* This will soon be converting from one type to another *)
+        arg_module
+      in
+      (* CR lmaurer: This "look for known name in path" code is duplicated
+         all over the place. *)
+      let basename = arg_import |> Compilation_unit.Name.to_string in
+      let arg_filename =
+        try
+          Load_path.find_uncap (basename ^ ".cmi")
+        with Not_found ->
+          raise(Error(Location.none, Env.empty,
+                      Cannot_find_argument_type arg_module)) in
+      let arg_sig =
+        Env.read_signature arg_module arg_filename ~add_binding:false in
+      if not (Env.is_parameter_unit arg_import) then
+        raise (Error (Location.none, env,
+                      Argument_for_non_parameter (arg_module, arg_filename)));
+      let coercion =
+        Includemod.compunit_as_argument env sourcefile actual_sig
+          arg_filename arg_sig
+      in
+      Some { ai_signature = arg_sig;
+             ai_coercion_from_primary = coercion;
+           }
+
 let type_implementation ~sourcefile outputprefix modulename initial_env ast =
   let error e =
     raise (Error (Location.in_file sourcefile, initial_env, e))
@@ -3408,18 +3446,24 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
         { structure = str;
           coercion = Tcoerce_none;
           shape;
-          signature = simple_sg
+          signature = simple_sg;
+          argument_interface = None;
         } (* result is ignored by Compile.implementation *)
       end else begin
         if !Clflags.as_parameter then
           error Cannot_compile_implementation_as_parameter;
+        let arg_type =
+          !Clflags.as_argument_for
+          |> Option.map Compilation_unit.Name.of_string
+        in
         let sourceintf =
           Filename.remove_extension sourcefile ^ !Config.interface_suffix in
         if !Clflags.cmi_file <> None || Sys.file_exists sourceintf then begin
+          let import = Compilation_unit.name modulename in
           let intf_file =
             match !Clflags.cmi_file with
             | None ->
-              let basename = modulename |> Compilation_unit.name_as_string in
+              let basename = import |> Compilation_unit.Name.to_string in
               (try
                 Load_path.find_uncap (basename ^ ".cmi")
               with Not_found ->
@@ -3427,15 +3471,34 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
                       Interface_not_compiled sourceintf)))
             | Some cmi_file -> cmi_file
           in
-          let import = Compilation_unit.name modulename in
           let dclsig =
             Env.read_signature import intf_file ~add_binding:false
           in
+          if Env.is_parameter_unit import then
+            error (Cannot_implement_parameter (import, intf_file));
+          let arg_type_from_cmi = Env.implemented_parameter import in
+          if not (Option.equal Compilation_unit.Name.equal
+                    arg_type arg_type_from_cmi) then
+            error (Inconsistent_argument_types
+                     { new_arg_type = arg_type; old_source_file = intf_file;
+                       old_arg_type = arg_type_from_cmi });
           let coercion, shape =
             Profile.record_call "check_sig" (fun () ->
               Includemod.compunit initial_env ~mark:Mark_positive
                 sourcefile sg intf_file dclsig shape)
           in
+          (* Check the _mli_ against the argument type, since the mli determines
+             the visible type of the module and that's what needs to conform to
+             the argument type.
+
+             This is somewhat redundant with the checking that was done when
+             compiling the .mli. However, this isn't just a boolean check - we
+             need to get the coercion out. An alternative would be to store the
+             coercion in the .cmi if we can sort out the dependency issues
+             ([Tcoerce_primitive] is a pain in particular). *)
+          let argument_interface =
+            check_argument_type_if_given initial_env intf_file dclsig arg_type
+          in
           Typecore.force_delayed_checks ();
           Typecore.optimise_allocations ();
           (* It is important to run these checks after the inclusion test above,
@@ -3452,7 +3515,8 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
           { structure = str;
             coercion;
             shape;
-            signature = dclsig
+            signature = dclsig;
+            argument_interface;
           }
         end else begin
           if !Clflags.as_parameter then
@@ -3466,6 +3530,9 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
           in
           check_nongen_signature finalenv simple_sg;
           normalize_signature simple_sg;
+          let argument_interface =
+            check_argument_type_if_given initial_env sourcefile simple_sg arg_type
+          in
           Typecore.force_delayed_checks ();
           Typecore.optimise_allocations ();
           (* See comment above. Here the target signature contains all
@@ -3477,7 +3544,7 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
             let alerts = Builtin_attributes.alerts_of_str ast in
             let name = Compilation_unit.name modulename in
             let kind =
-              Cmi_format.Normal { cmi_impl = modulename }
+              Cmi_format.Normal { cmi_impl = modulename; cmi_arg_for = arg_type }
             in
             let cmi =
               Profile.record_call "save_cmi" (fun () ->
@@ -3495,7 +3562,8 @@ let type_implementation ~sourcefile outputprefix modulename initial_env ast =
           { structure = str;
             coercion;
             shape;
-            signature = simple_sg
+            signature = simple_sg;
+            argument_interface
           }
         end
       end
@@ -3533,7 +3601,14 @@ let type_interface ~sourcefile modulename env ast =
     let uid = Shape.Uid.of_compilation_unit_id modulename in
     cms_register_toplevel_signature_attributes ~uid ~sourcefile ast
   end;
-  transl_signature env ast
+  let sg = transl_signature env ast in
+  let arg_type =
+    !Clflags.as_argument_for
+    |> Option.map Compilation_unit.Name.of_string
+  in
+  ignore (check_argument_type_if_given env sourcefile sg.sig_type arg_type
+          : Typedtree.argument_interface option);
+  sg
 
 (* "Packaging" of several compilation units into one unit
    having them as sub-modules.  *)
@@ -3633,8 +3708,12 @@ let package_units initial_env objfiles cmifile modulename =
         (Env.imports()) in
     (* Write packaged signature *)
     if not !Clflags.dont_write_files then begin
+      let cmi_arg_for =
+        (* Packs aren't supported as arguments *)
+        None
+      in
       let name = Compilation_unit.name modulename in
-      let kind = Cmi_format.Normal { cmi_impl = modulename } in
+      let kind = Cmi_format.Normal { cmi_impl = modulename; cmi_arg_for } in
       let cmi =
         Env.save_signature_with_imports ~alerts:Misc.Stdlib.String.Map.empty
           sg name kind (prefix ^ ".cmi") (Array.of_list imports)
@@ -3880,6 +3959,36 @@ let report_error ~loc _env = function
   | Cannot_compile_implementation_as_parameter ->
       Location.errorf ~loc
         "Cannot compile an implementation with -as-parameter."
+  | Cannot_implement_parameter(modname, _filename) ->
+      Location.errorf ~loc
+        "@[The interface for %a@ was compiled with -as-parameter.@ \
+         It cannot be implemented directly.@]"
+        Compilation_unit.Name.print modname
+  | Argument_for_non_parameter(param, path) ->
+      Location.errorf ~loc
+        "Interface %s@ found for module@ %a@ is not flagged as a parameter.@ \
+         It cannot be the parameter type for this argument module."
+        path
+        Compilation_unit.Name.print param
+  | Inconsistent_argument_types
+        { new_arg_type; old_source_file; old_arg_type } ->
+      let pp_arg_type ppf arg_type =
+        match arg_type with
+        | None -> Format.fprintf ppf "without -as-argument-for"
+        | Some arg_type ->
+            Format.fprintf ppf "with -as-argument-for %a"
+              Compilation_unit.Name.print arg_type
+      in
+      Location.errorf ~loc
+        "Inconsistent usage of -as-argument-for. Interface@ %s@ was compiled \
+         %a@ but this module is being compiled@ %a."
+        old_source_file
+        pp_arg_type old_arg_type
+        pp_arg_type new_arg_type
+  | Cannot_find_argument_type arg_type ->
+      Location.errorf ~loc
+        "Parameter module %a@ specified by -as-argument-for cannot be found."
+        Compilation_unit.Name.print arg_type
 
 let report_error env ~loc err =
   Printtyp.wrap_printing_env_error env
diff --git a/ocaml/typing/typemod.mli b/ocaml/typing/typemod.mli
index e7feb7dd6dd..adef32ad10b 100644
--- a/ocaml/typing/typemod.mli
+++ b/ocaml/typing/typemod.mli
@@ -42,11 +42,8 @@ val type_implementation:
   sourcefile:string -> string -> Compilation_unit.t -> Env.t ->
   Parsetree.structure -> Typedtree.implementation
 val type_interface:
-  sourcefile:string
-  -> Compilation_unit.t
-  -> Env.t
-  -> Parsetree.signature
-  -> Typedtree.signature
+  sourcefile:string -> Compilation_unit.t -> Env.t ->
+  Parsetree.signature -> Typedtree.signature
 val transl_signature:
         Env.t -> Parsetree.signature -> Typedtree.signature
 val check_nongen_signature:
@@ -155,6 +152,14 @@ type error =
   | Strengthening_mismatch of Longident.t * Includemod.explanation
   | Cannot_pack_parameter
   | Cannot_compile_implementation_as_parameter
+  | Cannot_implement_parameter of Compilation_unit.Name.t * Misc.filepath
+  | Argument_for_non_parameter of Compilation_unit.Name.t * Misc.filepath
+  | Cannot_find_argument_type of Compilation_unit.Name.t
+  | Inconsistent_argument_types of {
+      new_arg_type: Compilation_unit.Name.t option;
+      old_arg_type: Compilation_unit.Name.t option;
+      old_source_file: Misc.filepath;
+    }
 
 exception Error of Location.t * Env.t * error
 exception Error_forward of Location.error
diff --git a/ocaml/utils/clflags.ml b/ocaml/utils/clflags.ml
index aa76847be00..9221fdc6ae3 100644
--- a/ocaml/utils/clflags.ml
+++ b/ocaml/utils/clflags.ml
@@ -116,6 +116,7 @@ and transparent_modules = ref false     (* -trans-mod *)
 let unique_ids = ref true               (* -d(no-)unique-ds *)
 let locations = ref true                (* -d(no-)locations *)
 let as_parameter = ref false            (* -as-parameter *)
+and as_argument_for = ref None          (* -as-argument-for *)
 let dump_source = ref false             (* -dsource *)
 let dump_parsetree = ref false          (* -dparsetree *)
 and dump_typedtree = ref false          (* -dtypedtree *)
diff --git a/ocaml/utils/clflags.mli b/ocaml/utils/clflags.mli
index 2a2651aed31..82927b48ce7 100644
--- a/ocaml/utils/clflags.mli
+++ b/ocaml/utils/clflags.mli
@@ -127,6 +127,7 @@ val transparent_modules : bool ref
 val unique_ids : bool ref
 val locations : bool ref
 val as_parameter : bool ref
+val as_argument_for : string option ref
 val dump_source : bool ref
 val dump_parsetree : bool ref
 val dump_typedtree : bool ref
diff --git a/tools/flambda_backend_objinfo.ml b/tools/flambda_backend_objinfo.ml
index 602a55fcbde..03dbcffbb9e 100644
--- a/tools/flambda_backend_objinfo.ml
+++ b/tools/flambda_backend_objinfo.ml
@@ -68,6 +68,10 @@ let print_impl_import import =
 
 let print_line name = printf "\t%s\n" name
 
+let print_global_line glob =
+  (* Type will change soon for parameterised libraries *)
+  printf "\t%a\n" Compilation_unit.Name.output glob
+
 let print_name_line cu =
   printf "\t%a\n" Compilation_unit.Name.output (Compilation_unit.name cu)
 
@@ -113,6 +117,14 @@ let print_cmi_infos name crcs kind =
       | Parameter -> true
     in
     printf "Is parameter: %s\n" (if is_param then "YES" else "no");
+    begin
+      match kind with
+      | Normal { cmi_arg_for = Some arg_for; _ } ->
+        printf "Argument for parameter:\n";
+        print_global_line arg_for
+      | Normal _ | Parameter ->
+        ()
+    end;
     printf "Interfaces imported:\n";
     Array.iter print_intf_import crcs
   end