T2 with prescription T4

A friend of mine reciently asked me if he could take T2 to speed up his fat loss, however, he is already taking prescription T4 for low thyroid levels already, it is a relatively small dose (20mcg/day), but I didn’t want to make any recomendations until I heard from some pro’s. I know that if T3 levels are elevated that T4 production decreases as well as the converstion of T4 to T3,and I am not sure wether this thyroid would rebound after this,which would require him to up his daily dose of T4 perminately, but since T2 is less inhibitory can he still get away with using it?? I need some help from the pro’s here so I have some info to stop him from doing something stupid. Thanks!!!