Allogeneic Hematopoietic Stem Cell Transplantation for High-Risk Hematologic Malignancies Using One Haploidentical Donor

Inclusion Criteria: 1. This treatment is for patients with high risk hematologic malignancies. High risk is defined as: * Any patient with a hematologic malignancy with residual disease after treatment with 1 or more chemotherapy regimens in whom achievement of remission with additional chemoradiotherapy is felt to be unlikely * Patients without morphologic evidence of disease but with high risk features which would predict for relapse despite remission at HSCT such as adverse cytogenetics, 3rd or greater CR (complete response), or failure to recover peripheral blood counts to normal ranges. While these patients do not have detectable disease by current methods, like all patients they have non-detectable disease which in their case is highly aggressive. 2. Patients must have one related donor who is HLA (human leukocyte antigen) mismatched in the GVHD direction at two or more HLA loci 3. Patients must adequate organ function: * LVEF (left ventricular ejection fraction) of \>50 % * Diffusing capacity of the lungs for carbon monoxide (DLCO) (adjusted for hemoglobin) \>50 % of predicted and forced expiration to the full FEV-1 \>50 % * Adequate liver function as defined by a serum bilirubin \<1.8, AST (aspartate aminotransferase) or ALT (alanine aminotransferase) \< 2.5X upper limit of normal * Creatinine clearance of \> 60 ml/min 4. Karnofsky Performance Status (KPS) of \> 80% on the modified (KPS) tool 5. Patients must be willing to use contraception if they have childbearing potential 6. Able to give informed consent Exclusion Criteria: 1. Modified (KPS) Karnofsky Performance status of \<80% 2. \> 5 Comorbidity Points on the Hematopoietic cell transplantation - specific comorbidity (HCT-CI) Index (See Appendix B) 3. Class I or II antibodies against donor human leukocyte antigens (HLA) 4. HIV positive 5. Active involvement of the central nervous system with malignancy 6. Psychiatric disorder that would preclude patients from signing an informed consent 7. Pregnancy, or unwillingness to use contraception if they have child bearing potential 8. Patients with life expectancy of \< 6 months for reasons other than their underlying hematologic/oncologic disorder 9. Alemtuzumab treatment within 8 weeks of HSCT admission 10. Anti-thymocyte globulin (ATG) level of \> 2 ugm/ml 11. Patients with active inflammatory processes including T max \>101 or active tissue inflammation are excluded 12. Inability to tolerate cyclophosphamide or undergo total body irradiation at the doses specified in the treatment plan