In theory, Max4Live shouldn’t affect the MIDI functions of Max standalone. But I’ve noticed that Ableton Live sometimes seems to "steal" MIDI ports. It’s an issue (confirmed by others) which has nothing to do with Max4Live.
Basically you can use Live to route MIDI. Just create a MIDI track and select the corresponding input/output ports. Note however that channel information is not preserved. So for a general solution you’d need 16 tracks I guess.