CD8+ T Cell Depletion for GVHD Prophylaxis After Peripheral Blood Stem Cell Transplantation

The purpose of this trial is to determine if selectively removing only a small subset of T cells, called CD8+ T cells, is safe and if it can reduce the risk of graft versus host disease (GVHD) without losing the anti-cancer effects.

* The patient will be admitted to the hospital once a good donor is found for chemotherapy and stem cell transplant. The patient will remain in the hospital for 8 days and will receive two chemotherapy drugs (fludarabine and Busulfex) intravenously once each day for 4 days.
* On the third day after the patient has finished chemotherapy, the donor cells should arrive at Dana-Farber Cancer Institute and the lab will remove CD8 cells. Then the product will be given to the patient through a central line. If there are not enough stem cells in the donor product, then the CD8 cells will not be taken out, and the patient will get the whole product.
* Just before and after the transplant, the patient will also take tacrolimus and methotrexate to help prevent GVHD. Tacrolimus is a pill that will be taken orally two times a day. Methotrexate is a chemotherapy drug that is given intravenously on days 1, 3 and 6 after the transplant. In addition to the these drugs, participants will also take antibiotics to prevent infection and Filgrastim (G-CSF, neupogen) until their white blood cell counts are better.
* After the stem cell infusion, check-ups and blood tests will be performed at least once a week for 1 month. At about one month, a bone marrow biopsy to look for the donor's cells in the participants bone marrow will be performed. After the 1-month evaluation, the patient will be seen at least every 2 weeks with another bone marrow biopsy at 3-4 months after the transplant.
* After the patient is past 100 days since transplant, they will be followed in the clinic and have blood work done at least once a month until 6 months post transplant.
* The trial will end at 6 months after the transplant, but patients will be tracked for the rest of their life to look at long-term effects of this transplant.

Eligibility Criteria:
Inclusion Criteria:

* Hematologic malignancies that are candidates for allogeneic non-myeloablative stem cell transplantation
* AML or ALL in first or subsequent remission, or in resistant or untreated relapse with marrow blast \< 20% of cellularity
* CML in first or subsequent chronic phase, or accelerated phase
* Myelodysplastic syndrome with \< 20% marrow blasts
* NHL or Hodgkin's lymphoma in second or greater remission, or partial remission after salvage therapy, and in patients with marrow involvement, \<20% involvement in BM
* CLL RAI stage 2-4, which has progressed after initial fludarabine containing therapy, and BM involvement of \< 20%
* Multiple myeloma stage II-III, in first or subsequent plateau phase with \<20% BM plasma cells
* Available unrelated donor who is fully HLA matched at HLA-A,B,C and DRB1
* Age 18 or greater
* Performance status 0-2
* Life expectancy of \> 100 days
* No HLA-matched related donor available

Exclusion Criteria:

* Myeloproliferative disorders other than CML
* MDS with myeloproliferative features, or CMML
* High grade Burkitts or Burkitts-like Non-Hodgkin's lymphoma
* Prior allogeneic stem cell transplant
* Active CNS involvement with disease
* Uncontrolled infection
* Pregnancy
* Evidence of HIV infection
* Heart failure uncontrolled my medications
* Total bilirubin \> 2.0 mg/dl that is due to hepatocellular dysfunction
* AST \> 2 x institutional upper limit of normal
* Serum creatinine \> 2.0 mg/dl