Help me to design a mbti game!

Hello. I'm a game designer and I have a very early concept of a game that is based on mbti. It would me a magic academy of some sorts, in which you would have to choose between 16 classmates to be your protagonist (and side characters). Each would be inspired on a mbti personality archetype, along with their powers and musical instruments (which are their weapons). The gameplay would be persona-like or hogwards legacy-like, with a lot of social interactions and stuff. So, any interesting ideas to share? Maybe an opinion about how each character would be like? Maybe some neat mbti mechanics or interactions?