No. Installing third-party apps (like WordPress or Drupal) on the Adobe Commerce on cloud infrastructure servers is not allowed. You must host such applications on external servers.
The Adobe Commerce on cloud infrastructure Edition Terms of Service Agreement states the following in its Article 18:
Customer agrees that Adobe Commerce and the Service will not be used to host other third-party software applications that are not directly dependent on the Software.
Being a cloud solution, Adobe takes full responsibility for the security of your server. To guarantee high security, we only allow hosting the Adobe Commerce application on the dedicated cloud server.
As a PCI-certified Level 1 Solution Provider, Adobe Commerce on cloud infrastructure must follow the PCI Data Security Standard and make sure to:
… Develop and maintain secure systems and applications
(Adobe Approach to PCI Compliance Requirement 6, Maintain a Vulnerability Management Program)
Since Adobe cannot guarantee the PCI compliance of third-party applications, installing such apps on cloud servers is not allowed.
To improve the integration of your Adobe Commerce on cloud infrastructure application with the third-party solutions hosted on external servers, we encourage you to use the Commerce Marketplace extensions that might suit your purpose.