Nope, no distortion at all. What does "max" refer to? Are you aware that raising the level above "0" will likely cause digital distortion, depending on the music material...? Also, "loud" is rather subjective, I guess. I really wouldn't want to listen to the level that comes out of my DT880 at the settings you mention for more than a minute.... Even at the +4 setting, full level (0, not higher) can be uncomfortably loud.
[EDIT] Just tried my old original DT990 and DT880 from the Eighties, these are the 600 Ohm models. While the volume is lower, Hi Gain and full level is not something I'd want to listen to extensively... -8 is plenty loud... Depends on the source material of course. No distortion here, either. Both of them still incredibly good sounding headphones, by the way... 990 has more bass...
Re. source material: If you are mixing some soft classical/acoustic recordings pre-mastering it might be that you feel you're not getting enough volume. But whatever distortion might creep in while trying to raise levels would be digital, and not caused by an overload in the analog domain, either of the output or the phones. You can get enormous acoustic levels out of the DT880 Pro with the UCX witout any distortion. Beyond unpleasant, well into potentially ear-damaging.
Regards
Daniel Fuchs
RME