[badRNG]

I don't think it is all that uncommon for regular human-to-human transplant recipients to be on immunosuppressants for life. If I'm not mistaken, that's the case for all organ recipients, but there may be exceptions. I think the concept of "immunocompatibility" can refer to a spectrum of outcomes that we haven't gotten down even for transplants within our own species.

[giarc]

Yes all transplant patients receive immunosuppressants. The only transplant that wouldn't would be an allogenic stem cell transplants (uses the persons own stem cells), however these people typically don't have an immune system to begin with.