No, you have to choose which one you want. I think it is relatively easy to swap them if you get a different ended flagship headphone (or cable). But that's overkill just to listen to one night night on a different set.
There is no way real way to convert from the 4-pin XLR (balanced) headphone output to a 3-pin TRS (single-ended). You can't
tie the L- and R- lines together to GND on the TRS jack, as you'll short out the balanced output stage on the HPA module.
I'm thinking that you can add some series resistors to the L- and R- lines before tying them to GND, but I'm not sure about how
that will work out.
If your headphones that use the 4-pin XLR plug are ones that are something like the Senn 650, Senn 800, Audeze LCD2/3, HifiMan He-6, HE-500, HE-560, Abyss... they you might be pleasantly surprised by using a speaker out to 4-pin XLR jack - powering them from LIO's MOSFET AMP.
(and then you'd use the LIO HPA module for single-ended out).