Organ and Bone Marrow Transplantation?
As Mowgli pointed out, a bone marrow transplant involves destroying the patient's own immune system with radiation and, essentially, replacing it with a new one from the bone marrow donor. If you did a double kidney/bone marrow transplant from Alice into Bob, then Bob's new immune system (which is the same as Alice's) would recognize the new kidney from Alice as self (because it is) and not attack it. Yay!

The problem is that, to the new immune system, all the rest of Bob appears to be non-self and will get attacked. This is called Graft-versus-host disease and is at least as serious a problem as organ rejection.