The purpose of this research study is to examine the survival of patients undergoing partially matched hematopoietic stem cell transplant (HSCT) on a new type of treatment approach, which has been developed specifically for patients who have evidence of their disease at the time of transplant. In this research study, a way of strengthening the response of the donor cells against the disease has been developed. Patients will undergo one additional day between the two steps of the transplant which may allow their donor's cells to fight the disease more effectively.

This is a phase II study in which patients receive a haploidentical HSCT from a single donor. The period between the donor lymphocyte infusion (DLI) and tolerizing doses of CY has been extended to allow for an increased period of allogeneic response against tumor targets. The outcomes of patients undergoing this extra time period will be compared to historical data to assess efficacy.

Primary Objective:

1) To assess 1 year relapse free survival in patients undergoing hematopoietic stem cell transplant (HSCT) using the Thomas Jefferson University (TJU) 2 step approach with an extra day inserted between the DLI and administration of cyclophosphamide (CY).

Secondary Objectives:

1. To assess the consistency and pace of engraftment.
2. To assess the pace of T cell and B cell immune recovery.
3. To assess regimen related toxicity, (GVHD) graft-versus-host disease incidence and severity, and overall survival in patients undergoing treatment on this protocol. .
4. To assess the tolerance of the period of fever, diarrhea, and rash in each arm in an effort to determine whether a longer interval prior to cytoxan changes this side effect qualitatively compared to prior patient groups or concurrent patient groups. N.B. Patients with hematologic malignancies in remission will continue to be transplanted without modification to the original 2-step approach and will serve as a concurrent comparison group.
5. To collect leukemia samples prior to transplant and after relapse whenever possible. To assess the overall degree of HLA-class I and class II expression on these paired samples. To test for loss of one or both HLA haplotypes in the relapsed tumor specimens.
6. To determine the number of cluster of differentiation 4 (CD4+) cluster of differentiation 25 (CD25+) FOXP3+ regulatory cells post HSCT and to assess whether this is correlated with the development of GVHD after transplant.

Inclusion Criteria:

1. 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 or who is in 3rd or greater complete remission (CR).

   Patients with marrow based diseases in which the marrow biopsy does not meet criteria for active disease (ie <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 at least one related donor who is HLA mismatched in the GVHD direction at two or more HLA loci.

3. Patients must adequate organ function:

   1. Left ventricular ejection fraction (LVEF) of >50 %
   2. Diffusion capacity of the lung for carbon monoxide (DLCO) (adjusted for hemoglobin) >50 % of predicted
   3. Adequate liver function as defined by a serum bilirubin <1.8, Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 2.5 times upper limit of normal
   4. Creatinine clearance of > 60 ml/min

4. Karnofsky Performance Status 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 Karnofsky performance status (KPS) of <80%
2. > 5 Comorbidity Points on the hematopoietic cell transplantation comorbidity index (HCT-CI) Index
3. Untreated 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. Anti-thymocyte globulin (ATG) level of > 2 ugm/ml
11. Patients with active inflammatory processes including Tmax >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