Haploidentical hematopoietic stem cell transplant is a life-saving therapy for patients who are without well matched donors. This type of therapy has been associated with poor outcomes in the past due to complications such as infection. The Jefferson 2 Step approach was designed to allow the infusion of an exact dose of tolerized lymphocytes in haploidentical transplant in order to allow for immune reconstitution post transplant to avoid infectious complications while still having acceptable rates of GVHD. In this approach, patients with high-risk hematological malignancies undergo 8 fractions of TBI (12 Gy) followed by an exact dose of donor lymphocytes. The phase I portion of the study determined the optimal dose of lymphocytes. Two days after receiving the donor lymphocytes, the patients receive 2 daily doses of cyclophosphamide. One day after receiving cyclophosphamide, the patients receive stem cell from their donor. Tacrolimus and mycophenylate mofetil are used as GVHD prophylaxis.