Three issues -- impedance mismatch, sensitivity mismatch, and different listening levels.
So potentially you'll have an impedance mismatch, so try to pick phones of similar impedance. There could still be variations at certain frequencies that peak or dip at the same time, making things worse for the amp, and exaggerate a frequency issue that wasn't there with just one. Unlikely, but potentially a problem.
Sensitivity issue -- same results, slightly different cause (albeit related).
Listening levels -- previously discussed and self explanatory, I would hope.
We actually had this problem when we were doing some listening tests with an EAR headphone amp. The Sennheisers were much less sensitive than the Grados, so the person listening to the Sennheisers was at a disadvantage at being able to hear differences, much less anything. I have a reputation for listening at an entire notch lower than anyone else, but the difference was too much even for me. So don't think that you can necessarily cancel out the third problem with a judicious choice of headphones.