Why shouldn't it? XLR isn't even the limiting factor, it has been used with up to 7 pins.I was wondering about balanced stereo(does it even exist?).
It's differential signaling, each channel requires transmitting an inverted signal. You need 2x n + 1 cables/contacts for n channels (in some cases it might be possible to drop the GND line, but with a battery powered device it's probably not a good idea)...or would blanced stereo not work on a TRRS, would that require TRRRS?