Aside from the moral aspects, it's also interesting to think about the results. Would a new brain have difficulty operating a different body? Would one's senses translate similarly? Would the person's idea of where their limbs are in space be all messed up?
The functionality that hand transplant recipients obtain from the transplant apparently varies, but the results can be quite impressive. The Wikipedia article notes one recipient was able to use his transplanted hand to drink from a bottle of water a week after the procedure, and tie shoelaces after a few months.
If brains can successfully adapt to controlling a transplanted hand, under the right circumstances perhaps they can also adapt to multiple transplanted limbs, or a whole body.
[1] https://en.wikipedia.org/wiki/Hand_transplant#Long-term_func...