The drivers in the past have been looked at, they can't take much more than 3V, 3.2 seems to be the max without passing the extra voltage on to the diode and killing it.
It's hard to answer really, as the DX driver circuits are quite wonky and vary a lot between individual speciments too. The best way to go about is, if you ask me, to find out what the 'proper' current is, and not raising voltage beyond that point.
I've driven a DX20 from 4 volts or so without ill effect, but that had a bad driver (which worked better with the higher voltage). To be safe, i wouldn't exceed 3.0 volts, though some people claim they run well from 3.6 volt lithium cells.