YES! I will speak form first hand experience. I was dx with Graves back in 99, after about 5 years of yo yo weight up and down. I actually dropped 70 lbs in about 6 months time and my resting heart rate was over 120 bpm, which led to hospitalization, extensive bloodwork, the whole kit and kaboodle. Came back as Graves.

Then I had my daughter and shortly there after received a radioactive iodine treatment that was supposed to kill of my thyroid, or at least a part of it, which has now gone into hypothyroid disorder so yes, it is possible and there are a lot of reasons for this. Her body could naturally be over compensating.

I did just find out however that I actually have MS too. So mine could be from a combination of both. The best advise I can offer is to find a good endocrinologist and keep her treatments consistent which is something I did not do and I am now starting over from scratch.