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.

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