Chemotherapy and Unrelated Donor Stem Cell Transplantation for Patients With Cancers of the Blood and Immune System

Background: Major problems with stem cell transplantation (SCT) for cancer treatment are a lack of suitable donors for patients without a human leukocyte-antigen (HLA) tissue-matched sibling and graft-versus-host disease (GVHD), a serious side effects of immune-suppressing chemotherapy that is given to bring the cancer under control before SCT. In GVHD, the patients immune system attacks the transplanted donor cells. This study will try to improve the results of SCT from unrelated HLA-matched donors using targeted immune-depleting chemotherapy to bring the cancer under control before transplantation and to lower the chance of graft rejection, followed by reduced-intensity transplant chemotherapy to make the procedure less toxic. Objectives: To evaluate the safety and effectiveness of targeted immune-depleting chemotherapy followed by reduced-intensity transplant chemotherapy in patients with advanced cancers of the blood and immune system. To evaluate the safety and effectiveness of two different drug combinations to prevent GVHD. Both regimens have been successful in preventing GVHD, but they work by different mechanisms and affect the rebuilding of the immune system after the transplant. Eligibility: People 18 to 74 years of age with advanced or high-risk cancers of the blood and immune system who do not have a suitable HLA-matched sibling. Design: All patients receive chemotherapy before transplant to treat the cancer and suppress immune function. All patients receive a conditioning regimen of cyclophosphamide for 4 days and fludarabine for 4 days before SCT to prepare for the transplant. Patients are randomly assigned to one of two combination drug treatments to prevent GHVD as follows: * Group 1: Tacrolimus starting 3 days before SCT and continuing for 6 months, plus methotrexate on days 1, 3, 6, and 11 post-SCT, plus sirolimus starting 3 days before the SCT and continues for 6 months following SCT. * Group 2: Alemtuzumab for 4 days starting 8 days