A Research Study of Bone Marrow Transplantation From Unrelated or Partially Matched Related Donors

Inclusion Criteria: 1. Any patient with a hematological or oncological diagnosis in which allogeneic hematopoietic stem cell transplantation (HSCT) is thought to be beneficial. 1. Patients without morphological or molecular evidence of disease 2. For patients with "indolent diseases," if the patient has evidence of disease the disease burden must be minimal (at least PR) and the disease must be chemoresponsive. Thus for example patients with acute leukemia (not an indolent disease) must be in a morphological CR or CRp. 2. For patients with MDS the inclusion criteria is specifically as follows: * For patients with RA or RARS or isolated 5q- they can proceed to transplant without any treatment. * For patients with RAEB-1, RCMD+/-RS, or MDS NOS must have stable disease for 6 months (as documented by serial bone marrow examinations) in the absence of any therapy but growth factors or transfusion support. Patients who require treatment to "control their disease" must show chemo-responsiveness * For patients with CMML or RAEB-2 they must demonstrate chemo-responsiveness * Chemo-responsiveness is defined as a blast percentage decrease by at least 5 percentage points and there must be less than 10% blasts after treatment and at the time of transplant, if there are more than 10% blasts at any point during the disease course * Chemo-responsiveness must also include at least one of the following if applicable: * A cytogenetic response * A well-documented decrease in transfusion requirements. 3. Patients must have a related donor who is zero, one, two, three, or four antigen mismatched at the HLA-A; B; C; DR loci or an unrelated donor up to a two antigen mismatch. DNA will be retained by the tissue typing laboratory for possible typing for DQ and DP. When multiple related donor options are available donor selection will be determined the same as in the TJU two-step protocols. When multiple unrelated donors are available care will be made to avoid HLA-A and HLA-B mismatches if possible based on data from the Japanese Marrow Donor Registry studies. An HLA antibody screen will be performed on each patient. 4. All patients must have adequate organ function: 1. Patients with related donors must have an LVEF of \>35%. Patients with unrelated donors must have an LVEF \>45%. Patients with LVEF ≤50% and all patients with symptoms or history of heart failure or coronary artery disease must have a stress echo or equivalent test and a cardiological evaluation. 2. Patients with related donors must have a DLCO \>35% of predicted corrected for hemoglobin. Patients with unrelated donors must have a DLCO \>45% of predicted corrected for hemoglobin. For related donors if the DLCO is less than 45% the EF must be greater than 45% and vice versa. 3. Patients with related donors must have an adequate liver function as defined by a serum bilirubin \<3.0, AST and ALT \<3.0X upper limit of normal. Patients with unrelated donors must have an adequate liver function as defined by a serum bilirubin \<1.8, AST and ALT \< 2.5X upper limit of normal. Exceptions may be granted for patients with "benign" liver disorders such as Gilbert's disease. 4. Patients with related donors or with unrelated donors must have a creatinine clearance of \> 60 ml/min/1.73 m\^2. 5. Patients with related donors must have a performance status \> 60% (TJU Karnofsky14) (Appendix A). Patients with unrelated donors must have a Performance status \> 70% (TJU Karnofsky). 6. Patients with related donors must have a HCT-CI Score \< 6 Points (Appendix B). Patients with unrelated donors must have a HCT-CI Score \< 5 Points. 7. Patients must be willing to use contraception if they are of childbearing potential. 8. Patients must be able to give informed consent or have a care giver who can give consent. 9. Patients that are HIV positive will be eligible for the study if they have an undetectable viral load and meet the above criteria for patients with unrelated donors. Exclusion Criteria: 1. Patients with related donors who have a combination of Performance status of \< 70% (TJU Karnofsky) and an HCT-CI of 4 points or more. Patients with unrelated donors with a combination of Performance status of \< 80% (TJU Karnofsky) and an HCT-CI of 4 points or more. 2. Patients with active involvement of the central nervous system with malignancy. Patients with a disease with potential for CNS involvement should have documentation of the lack of CNS involvement via lumbar puncture or similar procedure performed within two months of admission or as per TJU standard practice guidelines. 3. Patients with a psychiatric disorder that would preclude patients from complying with the protocol even with a caregiver. Patients with a lack of social support that would interfere with the ability to receive appropriate medical care will also be excluded. 4. Pregnancy 5. Patients with life expectancy of \< 6 months for reasons other than their underlying hematological/oncological disorder. 6. Patients who have received alemtuzumab within 8 weeks of the transplant admission, or who have recently received horse or rabbit ant-thymocyte globulin and have an ATG level of \> 2 μg/ml. Patients on systemic corticosteroids at a dose equivalent of prednisone 7.5mg/day or higher. 7. Patients who cannot receive cyclophosphamide. 8. Patients with evidence of another malignancy, exclusive of a skin cancer that requires only local treatment, should not be enrolled on this protocol. 9. Patients with refractory disease. 10. Patients with clinically significant preformed antibodies to their donors. 11. Patients who require supplemental oxygen other than for sleep apnea will be excluded.