Patients who undergo a kidney transplant require prolonged therapy with drugs that suppress the immune system (called immunosuppressive regimens) to stop the immune system from attacking the transplanted kidney in order to limit damage to or the possibility of rejecting the transplanted kidney. The purpose of this study is to evaluate benefits and risks of two immunosuppressive regimens (belatacept with everolimus or tacrolimus with mycophenolate mofetil) following thymoglobulin induction and rapid corticosteroid withdrawal.