Well, in a way, you can use all 16 channels in BIAB (using the Sequencer feature); it's just that in addition to the ones BIAB already uses, they're only available on the Melodist or Soloist track as a multi-channel track. Each one of those channels can have it's own instrument, but you have to be using a GM synth that accepts standard patch numbers to set the instruments on the different channels. You have to be careful to work around the channels already used by any MIDI styles.
That being said, it would be much easier to manipulate the date if each channel had its own track, but as Bob said, you really are getting into DAW territory here. Not saying that BIAB couldn't do it, but it would be much more of a DAW, but just a different user interface than RealBand.
But back to the original post, I don't know why the RealTracks and RealDrums have to overlay the MIDI tracks. They should be separate. That would allow you to have a RealDrums track and a MIDI drums track. Better yet, be able to assign a RealDrum to any RealTrack. BIAB should be smart enough to know that it's a RealDrum and not transpose it when the chord grid changes.
Here was my original request back in early 2015 regarding this.