Well, you'd presumably have a connection to each of the servers in the form of a client factory and a protocol instance. Then, every time you get a message, you figure out which protocol instance you want (the one for the appropriate server) and send a message to it. You could do that with self.transport.write, of course, but it would be much easier to just use a ready-made RPC thing.
One such RPC thing is AMP, which comes with Twisted. You can read more about it here:
http://amp-protocol.net/https://twistedmatrix.com/documents/current/core/howto/amp.html
You will probably end up having a command like HandlePacket or something (presumably you can come up with a more apt domain-specific name), and something close to self.servers[serverFor(packet.origin)].callRemote(HandlePacket, packet.data), or whatever.
I realize this is still pretty vague and high level, so feel free to ask more questions about the parts that are unclear :)