Body Theory Of Personal Identity

Looking to the body theory to resolve personal identity tells us that we can be who we are because we still occupy the same body. The body theory believes that the only distinguishable thing about a person is their body.
Another thought is if the body theory consists of the whole body being what makes a person, then what about prosthetics, and other appearance surgeries? Would these not alter the being that we once were? I would say that they do, and yet we still are the person we once were, just with some plastic parts.
The brain theory says that where there is the same brain there is the same person. I would say this is also true. I would like to think that if my brain was put into another head that I would still have my thoughts, and my