diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index dc2a0fca..c1bae57d 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -2,12 +2,11 @@ name: test
 
 on:
   push:
-    branches: [main]
   pull_request:
-    branches: [main]
   schedule:
     # Midnight UTC:
     - cron: "0 0 * * *"
+  workflow_dispatch:
 
 jobs:
 
@@ -19,28 +18,23 @@ jobs:
       matrix:
         # Test all supported versions on Ubuntu:
         os: [ubuntu-latest]
-        python: ["3.7", "3.8", "3.9", "3.10", 3.11-dev, 3.12-dev]
+        # Skip 3.12-dev, pending https://github.com/python-greenlet/greenlet/issues/323
+        python: [pypy3.8, pypy3.9, "3.7", "3.8", "3.9", "3.10", 3.11-dev]
         include:
-          # Also test PyPy, macOS, and Windows:
-          - os: ubuntu-latest
-            python: pypy-3.9
-          - os: ubuntu-latest
-            python: pypy-3.8
-          - os: ubuntu-latest
-            python: pypy-3.7
+          # Also test macOS and Windows:
           - os: macos-latest
             python: "3.10"
           - os: windows-latest
             python: "3.10"
     steps:
-    - uses: actions/checkout@v2
+    - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python }}
-      uses: actions/setup-python@v2
+      uses: actions/setup-python@v4
       if: "!endsWith(matrix.python, '-dev')"
       with:
         python-version: ${{ matrix.python }}
     - name: Set up Python ${{ matrix.python }} using deadsnakes
-      uses: deadsnakes/action@v2.1.1
+      uses: deadsnakes/action@v3.0.0
       if: "endsWith(matrix.python, '-dev')"
       with:
         python-version: ${{ matrix.python }}