Similar setups are common outside Brazil for various reasons — see “virtualization” (I think it went from buzzword to commodity).
It is still technically possible to have both services on the same port, exactly as Jeff Atwood said: you run nginx on port 80 and make it dispatch to either Joomla or Discourse based on the request (google “nginx reverse proxy” for info). Most people do use different hostnames, but I suspect you could even use different directories for that.
But if you talk about “university policies”, you might not have the privileges for the right setup (although, if you can run Docker, that’s very confusing).