Board Thread:Questions and Answers/@comment-25001290-20160627214958/@comment-26091443-20170607003613

ShigenSurge wrote: monoma is able to use both bakugo and red riot's quirk in the second season of boku no hero academia. Monoma's power is copying Quirks for a short time and he explicitely can't use more than one simultaneously.

Honestly, I'm not really sure why this thread is here, the answer is pretty simple: under normal circumstances no. They've made it clear that people either inherent one of their parents' Quirks some hybrid combination of the two that counts as one.

Things get trickier when All For One is in the mix, but that hasn't been treated as normal. As as far as One For All goes: All Might has said that Nana had her own Quirk so presumably, no, having One For All doesn't make your own Quirk disappear (I don't know why you'd think it would anyway).

The point of all this is: the vast, vast majority of people in the story only have Quirk, and naturally having two is not considered possible.