diff --git a/.github/workflows/schedule_tests.yml b/.github/workflows/schedule_tests.yml
index 30c3734c4a..38f8db000c 100644
--- a/.github/workflows/schedule_tests.yml
+++ b/.github/workflows/schedule_tests.yml
@@ -37,7 +37,7 @@ jobs:
       - name: Run tests
         run: python tests/runtests.py -v2
 
-  pypy:
+  pypy-sqlite:
     runs-on: ubuntu-latest
     name: Ubuntu, SQLite, PyPy3.10
     continue-on-error: true
@@ -56,7 +56,44 @@ jobs:
         run: python -m pip install --upgrade pip setuptools wheel
       - run: python -m pip install -r tests/requirements/py3.txt -e .
       - name: Run tests
-        run: python tests/runtests.py -v2
+        run: python -Wall tests/runtests.py --verbosity=2
+
+  pypy-postgresql:
+    runs-on: ubuntu-latest
+    name: Ubuntu, PostgreSQL, PyPy3.10
+    continue-on-error: true
+    services:
+      postgres:
+        image: postgres:13-alpine
+        env:
+          POSTGRES_DB: django
+          POSTGRES_USER: user
+          POSTGRES_PASSWORD: postgres
+        ports:
+          - 5432:5432
+        options: >-
+          --health-cmd pg_isready
+          --health-interval 10s
+          --health-timeout 5s
+          --health-retries 5
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: pypy-3.10-nightly
+          cache: 'pip'
+          cache-dependency-path: 'tests/requirements/py3.txt'
+      - name: Install libmemcached-dev for pylibmc
+        run: sudo apt-get install libmemcached-dev
+      - name: Install and upgrade packaging tools
+        run: python -m pip install --upgrade pip setuptools wheel
+      - run: python -m pip install -r tests/requirements/py3.txt -r tests/requirements/postgres.txt -e .
+      - name: Create PostgreSQL settings file
+        run: mv ./.github/workflows/data/test_postgres.py.tpl ./tests/test_postgres.py
+      - name: Run tests
+        run: python -Wall tests/runtests.py --settings=test_postgres --verbosity=2
 
   javascript-tests:
     runs-on: ubuntu-latest