I think some organs have, but they need to be a match. I don’t think this would work for whole bodies. Hey, if they can give me an 18-year old body...
The Soviet dog grafts were of different breeds. I don't know if there was organ rejection (certainly the two heads nipped at each other until they realized that's how they were going to stay). My understanding is that they died after a period of weeks because of infection setting in, not organ rejection.
I seem to recall that they did the experiment several times.