A Two-Step Approach to Reduced Intensity Bone Marrow Transplant for Patients With Hematological Malignancies

Inclusion Criteria: 1. Any patient with hematologic or oncologic diagnosis in which allogeneic HSCT is thought to be beneficial, and in whom front-line therapy has already been applied. Patients treated on this protocol will be without morphological evidence of disease (complete remission or "CR"), or if the patient has evidence of disease, the patient must have had at least a good partial response (PR) to the most recent therapy and the disease must be chemoresponsive. 2. Patients treated on this study will have: * Acute leukemia in 1st or 2nd CR * MDS (myelodysplastic syndrome), specific subtypes of RA (refractory anemia) or RARS (refractory anemia with ringed sideroblasts) subtypes. * Hodgkin or Indolent Non-Hodgkin's lymphoma with chemosensitive disease * Myeloma without morphological evidence of disease, or a deep PR to the most recent therapy * Myeloproliferative disorders with at least a PR to current therapy * Aplastic Anemia * A hematological or oncological disease (not listed) that meets the criteria reviewed above (in CR or with a good PR). 3. Patients must have a related donor who is HLA mismatched at 2, 3, or 4 antigens at the HLA-A; B; C; DR loci in the GVHD direction. (Patients with related donors who are HLA identical or are a 1-antigen mismatch may be treated on this therapeutic approach, but will have their outcomes will not be part of the statistical aims of the study (see Summary section). 4. Patients must adequate organ function: * LVEF (Left ventricular end diastolic function) of \>50% * DLCO (Diffusing Capacity of the Lung for Carbon Monoxide ) ≥50% of predicted corrected for hemoglobin * Adequate liver function as defined by a serum bilirubin \<1.8, AST or ALT \< 2.5X upper limit of normal * Creatinine Clearance of ≥ 60 mL/min 5. Performance status ≥ 80% (TJU Karnofsky) for patients ≥ 60 years old or ≥70% for patients \< 60 years old. 6. HCT-CI Score ≤ 4 points for patients ≥ 60 years old or ≤ 5 points for patients \< 60 years old. 7. Patients must be willing to use contraception if they have childbearing potential 8. Able to give informed consent Exclusion Criteria: 1. Performance status \< 80% (TJU Karnofsky) for patients ≥ 60 years old or \<70% for patients \< 60. 2. Hematopoietic Cell Transplant-Comorbidity Index (HCT-CI) Score \> 4 points for patients ≥ 60 years old or \> 5 points for patients \< 60. 3. HIV positive 4. Active involvement of the central nervous system with malignancy 5. Inability to obtain informed consent 6. Pregnancy 7. Patients with life expectancy of \< 6 months for reasons other than their underlying hematologic/oncologic disorder 8. Patients who have received alemtuzumab within 8 weeks of the transplant admission, or who have recently received horse or rabbit anti-thymocyte globulin and have an anti-thymocyte globulin level of \> 2 ugm/ml 9. Patients with evidence of another malignancy, exclusive of a skin cancer that requires only local treatment, should not be enrolled on this protocol