diff --git a/.github/workflows/pytest.yaml b/.github/workflows/pytest.yaml
index e12585f667..1670d58a47 100644
--- a/.github/workflows/pytest.yaml
+++ b/.github/workflows/pytest.yaml
@@ -23,42 +23,45 @@ jobs:
   pytest:
     strategy:
       matrix:
-        include:
         # One job per OS; latest python version testable on GitHub actions.
         # These should match the versions used in the "pytest" workflows of both
         # ixmp and message_ix.
-        - os: macos-latest
-          python-version: "3.10"
-        - os: ubuntu-latest
-          python-version: "3.10"
-        - os: windows-latest
-          python-version: "3.9"
+        version:
+        - { os: macos-latest, python: "3.10" }
+        - { os: ubuntu-latest, python: "3.10" }
+        - { os: windows-latest, python: "3.9" }
+        upstream-version:
+        - v3.2.0  # Minimum version given in setup.cfg
+        - v3.5.0  # Latest released version
+        - main    # Development version
 
       fail-fast: false
 
-    runs-on: ${{ matrix.os }}
-    name: ${{ matrix.os }}-py${{ matrix.python-version }}
+    runs-on: ${{ matrix.version.os }}
+    name: ${{ matrix.version.os }}-py${{ matrix.version.python }}-upstream-${{ matrix.upstream-version }}
 
     steps:
     - name: Cancel previous runs that have not completed
       uses: styfle/cancel-workflow-action@0.9.1
 
     - name: Check out ixmp
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
       with:
         repository: iiasa/ixmp
+        ref: ${{ matrix.upstream-version }}
         path: ixmp
         fetch-depth: ${{ env.depth }}
 
     - name: Check out message-ix
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
       with:
         repository: iiasa/message_ix
+        ref: ${{ matrix.upstream-version }}
         path: message-ix
         fetch-depth: ${{ env.depth }}
 
     - name: Check out message-ix-models
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
       with:
         path: message-ix-models
         fetch-depth: ${{ env.depth }}
@@ -70,20 +73,21 @@ jobs:
         (cd message-ix-models; git fetch --tags --depth=${{ env.depth }})
       shell: bash
 
-    - uses: actions/setup-python@v2
+    - uses: actions/setup-python@v3
       with:
-        python-version: ${{ matrix.python-version }}
+        python-version: ${{ matrix.version.python }}
+
+    - name: Locate pip cache directory
+      id: pip-cache
+      run: echo "::set-output name=dir::$(pip cache dir)"
 
     - name: Cache Python packages and GAMS installer
-      uses: actions/cache@v2
+      uses: actions/cache@v3
       with:
-        path: |
-          ~/.cache/pip
-          ~/Library/Caches/pip
-          ~/appdata/local/pip/cache
-        key: ${{ matrix.os }}-py${{ matrix.python-version }}
+        path: ${{ steps.pip-cache.outputs.dir }}
+        key: ${{ matrix.version.os }}-py${{ matrix.version.python }}
         restore-keys: |
-          ${{ matrix.os }}-
+          ${{ matrix.version.os }}
 
     - uses: iiasa/actions/setup-gams@main
       with:
@@ -104,12 +108,12 @@ jobs:
       run: pytest message_ix_models -rA --verbose --color=yes --cov-report=xml --cov-report=term-missing
 
     - name: Test documentation build using Sphinx
-      if: ${{ startsWith(matrix.os, 'ubuntu') }}
+      if: startsWith(matrix.os, 'ubuntu')
       env:
         RTD_TOKEN_MESSAGE_DATA: ${{ secrets.RTD_TOKEN_MESSAGE_DATA }}
       run: make --directory=message-ix-models/doc html
 
     - name: Upload test coverage to Codecov.io
-      uses: codecov/codecov-action@v2
+      uses: codecov/codecov-action@v3
       with:
         directory: message-ix-models