Donor T Cells in Treating Patients With High-Risk Hematologic Cancer Undergoing Donor Peripheral Blood Stem Cell Transplant

Inclusion Criteria: * Diagnosis of a high-risk hematologic malignancy, including any of the following: * Acute lymphocytic leukemia * Acute myelocytic leukemia * Chronic myelogenous leukemia * Myelodysplastic syndrome * Non-Hodgkin lymphoma * Multiple myeloma * Meet eligibility criteria and co-enrolled in one of the following University of Minnesota protocols: * MT2001-02 consisting of myeloablative prep (cyclophosphamide and total body irradiation) followed by HLA-identical sibling peripheral blood progenitor cells (PBPC) transplantation * MT2001-10 consisting of nonmyeloablative prep (cyclophosphamide, fludarabine and total body irradiation) followed by HLA-identical sibling PBPC transplantation * Voluntarily written informed consent * Must have an HLA-identical sibling donor available, meeting the following criteria: * 12 to 75 years of age, \>40 kg body weight and in good health * Matched to recipient for HLA-A, B,DRB1 identical sibling match to recipient * Must be able and willing to have a separate apheresis collection performed on day -21 for the purposes of this study (in addition to the apheresis required for the transplant protocol) * Human immunodeficiency virus nucleic acid testing (HIV-NAT) negative, Human T-lymphotropic virus 1 (HTLV-1), HTLV-2 negative, hepatitic B and C negative Exclusion Criteria: * Not pregnant or nursing