Can we authenticate to PostgreSQL with TLS cert AND password for the same connection?

I want to configure my PostgreSQL server to enable authentication with TLS certificate and password at the same time (for the same connection, not just enable the two authentication mechanisms). Then for a client to authenticate, it must : - provide a valid certificate with the username set in the common name and signed by a trusted root ca - provide a password for this specific user I want to do this to improve safety. This way, even if my client certificate or my root CA are leaked, you still need a password to authenticate. I can't find out how to do that. In this page of the PostgreSQL documentation , it is said that when you use TLS certificate : > No password prompt will be sent to the client Then is it even possible to do this and if yes, how ?