Yes, you can do this with paramiko.
If you're connecting to one server, you can run multiple channels through a single connection. If you're connecting to multiple servers, you can start multiple connections in separate threads. No need to manage multiple processes, although you could substitute the multiprocessing module for the threading module and have the same effect.
I haven't looked into twisted conch in a while, but it looks like it getting updates again, which is nice. I couldn't give you a good feature comparison between the two, but I find paramiko is easier to get going. It takes a little more effort to get into twisted, but it could be well worth it if you're doing other network programming.