This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. This trial is studying the drug BMS-224818 which represents a new class of therapeutic agents that block the second signal required for T cell activation in an immune response. Safely controlling the recipient T cell response to a donor allograft is key to achieving normal function and long-term survival and function of a transplanted organ. Nanve T cells require signals through both the T cell receptor and a costimulatory receptor for full activation. CD28 is a key T cell costimulatory receptor molecule. BMS-224818 (LEA29Y) binds to CD80 and CD86, the ligands for CD28, thereby preventing full T cell activation and potentially inducing antigen-specific T cell hyporesponsiveness. Allogeneic transplant organ recipients can be treated with costimulation-blocking drugs like BMS-224818 prior to exposure to donor antigen, manipulating nanve T cell responses which are more susceptible to costimulation blockade than previously activated T cells. This is a two-year extension study (Amendment #3) of the main BMS study (GCO#00-1105) that is being conducted in the GCRC currently. If safety & efficacy are acceptable, maintenance dosing may be continued until year 2004.