It is possible and most people are on a mood stabilizer too.

Me personally I can't take AD with or w/o mood stabilizers but that's me. Every single person with any MI reacts differently to psych meds, so it's something like trial and error to find what works for you. Pdocs though have experience with different people and can usually figure out where to start once they know your diagnose and past experiences with meds.

Good luck.