diff --git a/.github/update-published-charms-tests-workflow.py b/.github/update-published-charms-tests-workflow.py
new file mode 100755
index 000000000..d604d6a61
--- /dev/null
+++ b/.github/update-published-charms-tests-workflow.py
@@ -0,0 +1,132 @@
+#! /usr/bin/env python
+
+# Copyright 2024 Canonical Ltd.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Update a GitHub workload that runs `tox -e unit` on all published charms.
+
+Charms that are not hosted on GitHub are skipped, as well as any charms where
+the source URL could not be found.
+"""
+
+import json
+import logging
+import pathlib
+import re
+import typing
+import urllib.error
+import urllib.parse
+import urllib.request
+
+logger = logging.getLogger(__name__)
+
+
+URL_BASE = 'https://api.charmhub.io/v2/charms/info'
+WORKFLOW = pathlib.Path(__file__).parent / 'workflows' / 'published-charms-tests.yaml'
+
+SKIP = {
+    # Handled by db-charm-tests.yaml
+    'postgresql-operator',
+    'postgresql-k8s-operator',
+    'mysql-operator',
+    'mysql-k8s-operator',
+    # Handled by hello-charm-tests.yaml
+    'hello-kubecon',  # Not in the canonical org anyway (jnsgruk).
+    'hello-juju-charm',  # Not in the canonical org anyway (juju).
+    # Handled by observability-charms-tests.yaml
+    'alertmanager-k8s-operator',
+    'prometheus-k8s-operator',
+    'grafana-k8s-operator',
+    # This has a redirect, which is too complicated to handle for now.
+    'bundle-jupyter',
+    # The charms are in a subfolder, which this can't handle yet.
+    'jimm',
+    'notebook-operators',
+    # Not ops.
+    'charm-prometheus-libvirt-exporter',
+    'juju-dashboard',
+    'charm-openstack-service-checks',
+}
+
+
+def packages():
+    """Get the list of published charms from Charmhub."""
+    logger.info('Fetching the list of published charms')
+    url = 'https://charmhub.io/packages.json'
+    with urllib.request.urlopen(url, timeout=120) as response:  # noqa: S310 (unsafe URL)
+        data = response.read().decode()
+        packages = json.loads(data)['packages']
+    return packages
+
+
+def get_source_url(charm: str):
+    """Get the source URL for a charm."""
+    logger.info("Looking for a 'source' URL for %s", charm)
+    try:
+        with urllib.request.urlopen(  # noqa: S310 (unsafe URL)
+            f'{URL_BASE}/{charm}?fields=result.links', timeout=30
+        ) as response:
+            data = json.loads(response.read().decode())
+            return data['result']['links']['source'][0]
+    except (urllib.error.HTTPError, KeyError):
+        pass
+    logger.info("Looking for a 'bugs-url' URL for %s", charm)
+    try:
+        with urllib.request.urlopen(  # noqa: S310 (unsafe URL)
+            f'{URL_BASE}/{charm}?fields=result.bugs-url', timeout=30
+        ) as response:
+            data = json.loads(response.read().decode())
+            return data['result']['bugs-url']
+    except (urllib.error.HTTPError, KeyError):
+        pass
+    logger.warning('Could not find a source URL for %s', charm)
+    return None
+
+
+def url_to_charm_name(url: typing.Optional[str]):
+    """Get the charm name from a URL."""
+    if not url:
+        return None
+    parsed = urllib.parse.urlparse(url)
+    if parsed.netloc != 'github.com':
+        logger.info('URL %s is not a GitHub URL', url)
+        return None
+    if not parsed.path.startswith('/canonical'):
+        # TODO: Maybe we can include some of these anyway?
+        # 'juju-solutions' and 'charmed-kubernetes' seem viable, for example.
+        logger.info('URL %s is not a Canonical charm', url)
+        return None
+    try:
+        return urllib.parse.urlparse(url).path.split('/')[2]
+    except IndexError:
+        logger.warning('Could not get charm name from URL %s', url)
+        return None
+
+
+def main():
+    """Update the workflow file."""
+    logging.basicConfig(level=logging.INFO)
+    charms = [url_to_charm_name(get_source_url(package['name'])) for package in packages()]
+    charms = [charm for charm in charms if charm and charm not in SKIP]
+    charms.sort()
+    with WORKFLOW.open('r') as f:
+        workflow = f.read()
+    repos = '\n'.join(f'          - charm-repo: canonical/{charm}' for charm in charms)
+    workflow = re.sub(r'(\s{10}- charm-repo: \S+\n)+', repos + '\n', workflow, count=1)
+    with WORKFLOW.open('w') as f:
+        f.write(workflow)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/.github/workflows/published-charms-tests.yaml b/.github/workflows/published-charms-tests.yaml
new file mode 100644
index 000000000..d7430de06
--- /dev/null
+++ b/.github/workflows/published-charms-tests.yaml
@@ -0,0 +1,131 @@
+# To update the list of charms included here, run:
+# python .github/update-published-charms-tests-workflow.py
+
+name: Broad Charm Compatibility Tests
+
+on:
+  schedule:
+    - cron: '0 1 25 * *'
+  workflow_dispatch:
+
+jobs:
+  charm-tests:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - charm-repo: canonical/content-cache-k8s-operator
+          - charm-repo: canonical/data-platform-libs
+          - charm-repo: canonical/dex-auth-operator
+          - charm-repo: canonical/discourse-k8s-operator
+          - charm-repo: canonical/grafana-agent-k8s-operator
+          - charm-repo: canonical/hardware-observer-operator
+          - charm-repo: canonical/identity-platform-login-ui-operator
+          - charm-repo: canonical/indico-operator
+          - charm-repo: canonical/jenkins-agent-k8s-operator
+          - charm-repo: canonical/jenkins-agent-operator
+          - charm-repo: canonical/kafka-operator
+          - charm-repo: canonical/livepatch-k8s-operator
+          - charm-repo: canonical/loki-k8s-operator
+          - charm-repo: canonical/manual-tls-certificates-operator
+          - charm-repo: canonical/mongodb-operator
+          - charm-repo: canonical/mysql-router-k8s-operator
+          - charm-repo: canonical/namecheap-lego-k8s-operator
+          - charm-repo: canonical/nginx-ingress-integrator-operator
+          - charm-repo: canonical/oathkeeper-operator
+          - charm-repo: canonical/oauth2-proxy-k8s-operator
+          - charm-repo: canonical/openfga-operator
+          - charm-repo: canonical/pgbouncer-k8s-operator
+          - charm-repo: canonical/ranger-k8s-operator
+          - charm-repo: canonical/route53-lego-k8s-operator
+          - charm-repo: canonical/s3-integrator
+          - charm-repo: canonical/saml-integrator-operator
+          - charm-repo: canonical/seldon-core-operator
+          - charm-repo: canonical/self-signed-certificates-operator
+          - charm-repo: canonical/smtp-integrator-operator
+          - charm-repo: canonical/superset-k8s-operator
+          - charm-repo: canonical/temporal-admin-k8s-operator
+          - charm-repo: canonical/temporal-k8s-operator
+          - charm-repo: canonical/temporal-ui-k8s-operator
+          - charm-repo: canonical/temporal-worker-k8s-operator
+          - charm-repo: canonical/traefik-k8s-operator
+          - charm-repo: canonical/trino-k8s-operator
+          - charm-repo: canonical/wordpress-k8s-operator
+          - charm-repo: canonical/zookeeper-operator
+    steps:
+      - name: Checkout the ${{ matrix.charm-repo }} repository
+        uses: actions/checkout@v4
+        with:
+          repository: ${{ matrix.charm-repo }}
+
+      - name: Checkout the operator repository
+        uses: actions/checkout@v4
+        with:
+          path: myops
+
+      - name: Install patch dependencies
+        run: pip install poetry~=1.6
+
+      - name: Update 'ops' dependency in test charm to latest
+        run: |
+          rm -rf myops/test
+          if [ -e "test-requirements.txt" ]; then
+            sed -i -e "/^ops[ ><=]/d" -e "/canonical\/operator/d" -e "/#egg=ops/d" test-requirements.txt
+            echo -e "\ngit+$GITHUB_SERVER_URL/$GITHUB_REPOSITORY@$GITHUB_SHA#egg=ops" >> test-requirements.txt
+          fi
+          if [ -e "requirements-charmcraft.txt" ]; then
+            sed -i -e "/^ops[ ><=]/d" -e "/canonical\/operator/d" -e "/#egg=ops/d" requirements-charmcraft.txt
+            echo -e "\ngit+$GITHUB_SERVER_URL/$GITHUB_REPOSITORY@$GITHUB_SHA#egg=ops" >> requirements-charmcraft.txt
+          fi
+          if [ -e "requirements.txt" ]; then
+            sed -i -e "/^ops[ ><=]/d" -e "/canonical\/operator/d" -e "/#egg=ops/d" requirements.txt
+            echo -e "\ngit+$GITHUB_SERVER_URL/$GITHUB_REPOSITORY@$GITHUB_SHA#egg=ops" >> requirements.txt
+          elif [ -e "poetry.lock" ]; then
+            sed -i -e "s/^ops[ ><=].*/ops = {path = \"myops\"}/" pyproject.toml
+            poetry lock --no-update
+          else
+            echo "Error: No requirements.txt or poetry.lock file found"
+            exit 1
+          fi
+
+      - name: Install dependencies
+        run: pip install tox~=4.2
+
+      - name: Run the charm's unit tests
+        run: tox -vve unit
+
+  charmcraft-profile-tests:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - profile: machine
+          - profile: kubernetes
+          - profile: simple
+    steps:
+      - name: Install charmcraft
+        run: sudo snap install charmcraft --classic
+
+      - name: Charmcraft init
+        run: charmcraft init --profile=${{ matrix.profile }} --author=charm-tech
+
+      - name: Checkout the operator repository
+        uses: actions/checkout@v4
+        with:
+          path: myops
+
+      - name: Update 'ops' dependency in test charm to latest
+        run: |
+          rm -rf myops/test
+          if [ -e "requirements.txt" ]; then
+            sed -i -e "/^ops[ ><=]/d" -e "/canonical\/operator/d" -e "/#egg=ops/d" requirements.txt
+            echo -e "\ngit+$GITHUB_SERVER_URL/$GITHUB_REPOSITORY@$GITHUB_SHA#egg=ops" >> requirements.txt
+          fi
+
+      - name: Install dependencies
+        run: pip install tox~=4.2
+
+      - name: Run the charm's unit tests
+        run: tox -vve unit
diff --git a/.github/workflows/tiobe.yaml b/.github/workflows/tiobe.yaml
index 350906522..6456792a8 100644
--- a/.github/workflows/tiobe.yaml
+++ b/.github/workflows/tiobe.yaml
@@ -1,6 +1,7 @@
 name: TIOBE Quality Checks
 
 on:
+  workflow_dispatch:
   schedule:
     - cron:  '0 7 1 * *'