Some idle surfing today has shown some headphone amps with a balanced output. Either 2 X 3 pin XLRs or 4 pin XlRs. The Little Dot mkvi+ has it on the front panel.
Every headphone I've seen terminates in a 3.5 or 6.3mm jack. Some headphones have detachable cables but in looking for a replacement cable with XLRs they either seem to be home made efforts or some mod done by a specialist company for a price. I coldn't find any mini XLRs to 4 pin XLRs at all that could be used with say AKG K702s. There also seems to be a need to mod the headphones themselves.
Is there much difference between using a balanced cable and just the normal headphone jack?