I am on thyroxine and take magnesium, vitamin D/calcium combined and vitamin B12 with no problems but I take them in the afternoon as I take the thyroxin in the morning.
Thypatient is right.....make sure any supplement is taken at least 4 hours away from thyroxine so there are no absorbancy problems with the thyroxine.
I can't address the overactive thyroid aspect, but can say I am on thyroxine too and also safely take magnesium/calcium. One thing to remember though is to make sure you space those supplements at least 4 hours away from taking the thyroxine.
Good luck.