A Two-Step Approach to Bone Marrow Transplant Using Cells From Two Partially-Matched Relatives

Inclusion Criteria:

1. Any patient with a hematologic malignancy with residual disease (morphological, cytogenetic, molecular, or radiographic) after treatment with 1 or more chemotherapy regimens in whom achievement of remission with additional chemoradiotherapy is felt to be unlikely or who is in 3rd or greater CR. Patients with marrow based diseases in which the marrow biopsy does not meet criteria for active disease (i.e. \<5% blasts in acute leukemia) but who does not have full count recovery will be eligible for treatment on this high risk trial.
2. Patients must have two related donors that meet an acceptable scenario as described above.
3. Patients must adequate organ function:

   * LVEF of \>= 50%
   * DLCO (adjusted for hemoglobin) \>= 50% of predicted
   * 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
4. Karnofsky Performance Status of \> 80 % on the modified KPS tool (see Appendix A).
5. Patients must be willing to use contraception if they have childbearing potential.
6. Able to give informed consent

Exclusion Criteria:

1. Modified KPS of \< 80%
2. \>= 5 Comorbidity Points on the HCT-CI Index (See Appendix B)
3. Class I or II antibodies against donor HLA antigens
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. ATG level of \>= 2 ugm/ml
11. Patients with active inflammatory processes (such as flair of an autoimmune disease) 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.