A recent development of immunosuppressive protocols (or simply, suppressants) offers a new option to patients suffering from end-stage renal disease: transplants from biologically incompatible donors. Suppressants are currently being used for direct transplants within patient-donor pairs, but they can be utilized more efficiently when combined with kidney exchanges. To assess the welfare gains from doing so, we introduce the "minimum chains algorithms" for different sizes of feasible exchanges. Using these algorithms, we calculate the minimal number of suppressants needed for transplants for a group of patient-donor pairs. Our simulation results show that (i) a significant reduction of suppressants can be achieved by implementing this proposal, (ii) it suffices to arrange 2-way exchanges for the best use of suppressants, and (iii) the welfare gain varies with the ABO blood-type distribution, and the gain in Korea appears to be larger than that in the United States. Finally, we assess the value (or cost) of each patient-donor pair by comparing the outcomes of the pools with and without the pair.