Thanks for your reply. To give more context: I am contributing to a Postgres driver used by a programming language. We are currently trying to understand what is legal/not legal to be sent through this connection.
In the documentation it states that the simple query protocol is followed on these connections, which is why we assumed a multi-command statement would work. I just wanted to make sure we are not doing anything wrong and that it is disallowed by design. We can, for instance, send "SELECT 1;" and receive a result.
I have a situation where I've set up a replication connection and tried to issue a query with the simple protocol that has multiple commands "SELECT 1; SELECT 2;".
What do you mean by "I've set up a replication connection"? IIUC they are not intended for interactive usage, they are intended for system-to-system data replication. If you want to issue queries just connect with a "normal connection".