They already can reconnect limbs and other body parts https://en.wikipedia.org/wiki/Replantation.

The problem like always is reconnecting the nerves which isn't something you have to worry about when transplanting organs.

If say you transplant a heart that heart will never talk to the recipients brain it will always continue to function on it's own, this also means that the brain cannot regulate the heart functions through the nervous system so mental states do not affect the hearts operations as they would with most people, hormonal neurotransmitters like adrenaline will still work tho.