The purpose of this study is to develop a way of treating patients who do not have a completely matched family donor or a readily available unrelated donor with bone marrow transplant by using a partially-matched family donor. Patients receiving this type of transplant will receive chemotherapy and/or radiation to treat their disease. They will also receive their donor's cells in 2 parts. During the first part, the donor's lymphocytes will be exposed to one of the chemotherapy agents to help the patient become tolerant to the lymphocytes. In the second part of the transplant, the patient will receive their donor's stem cells to help recover their peripheral blood counts and establish long-term engraftment. The hypothesis of this study is that in partially-matched allogeneic transplant, there is a defined number of donor T-cells that can be treated and given to the recipient to avoid post-transplant infection without causing severe graft-versus-host disease.

Haploidentical hematopoietic stem cell transplant is a life-saving therapy for patients who are without well matched donors. This type of therapy has been associated with poor outcomes in the past due to complications such as infection. The Jefferson 2 Step approach was designed to allow the infusion of an exact dose of tolerized lymphocytes in haploidentical transplant in order to allow for immune reconstitution post transplant to avoid infectious complications while still having acceptable rates of GVHD. In this approach, patients with high-risk hematological malignancies undergo 8 fractions of TBI (12 Gy) followed by an exact dose of donor lymphocytes. The phase I portion of the study determined the optimal dose of lymphocytes. Two days after receiving the donor lymphocytes, the patients receive 2 daily doses of cyclophosphamide. One day after receiving cyclophosphamide, the patients receive stem cell from their donor. Tacrolimus and mycophenylate mofetil are used as GVHD prophylaxis.

Inclusion Criteria:

1. Any patient with a hematologic or oncologic diagnosis in which allogeneic HSCT is thought to be beneficial, and in whom front-line therapy has already been applied.

2. Patients must have a related donor who is either a one, two or three out of six antigen mismatch at the HLA-A;B;DR loci.

3. Patients without a well-matched unrelated donor or those who have a disease status that precludes a wait for an identified unrelated donor.

4. Patients must adequate organ function:

   • LVEF of >45%
   • FVC or FEV1 >45% of predicted
   • Adequate liver function as defined by a serum bilirubin <1.8, AST or ALT < 2.5X upper limit of normal
   • Serum creatinine < 2.0 mg/dl or creatinine clearance of > 40 ml/min

5. Performance status > 60% (Karnofsky)

6. Patients must be willing to use contraception if they have childbearing potential

7. Able to give informed consent

Exclusion Criteria:

1. An eligible HLA-identical sibling donor.
2. Performance status < 60% (Karnosfsky)
3. HIV positive
4. Active involvement of the central nervous system with malignancy
5. Psychiatric disorder that would preclude patients from signing an informed consent
6. Pregnancy
7. Patients with life expectancy of < 6 months for reasons other than their underlying hematologic/oncologic disorder.