more network connections simultaneously

[wysota]

You could use different ports (like FTP does), but IMO it isn't necessary. Just add another command to your protocol that will allow clients to choose connection type. For example "CHAT MODE" would switch the connection into chat connection, while "CONTROL MODE" --- into connection that controls the session.

Or provide control sequences made of unused characters (and escape them during normal transmission) so that you don't have to handle different "modes".

To be honest this should be simply realised as urgent data (TCP) but I doubt Qt allows one to send/receive them.

Edit: Another way could be to provide "commands" between the client and the server and treat chat transmission as another command in network traffic.