Donor Lymphocyte Infusion in Treating Patients With Recurrent or Persistent Hematologic Cancer After Donor Stem Cell Transplant

DISEASE CHARACTERISTICS: * Has undergone allogeneic stem cell transplantation (ASCT) for hematologic malignancy at least 30 days ago * No failure to engraft following transplant * No active acute or chronic graft-versus-host disease (GVHD) * Minimal GVHD allowed * Persistent or relapsed disease after ASCT, including 1 of the following: * Chronic myelogenous leukemia (CML), meeting any of the following criteria: * Molecular relapse (may be treated with imatinib mesylate after transplant), as defined by any of the following: * ASCT was non-T-cell depleted, a negative bcr/abl was documented by PCR post-transplant, and bcr/abl is now detectable by 2 consecutive PCR determinations \> 30 days apart * ASCT was non-T-cell depleted and bcr/abl is detectable by PCR at any time after day 180 post-transplant * Cytogenetic relapse after 3-6 months of imatinib mesylate * Relapsed chronic phase, accelerated phase, or blastic phase CML after 3-6 months of imatinib mesylate * Must currently be in chronic phase or accelerated phase CML only * Patients with blastic phase CML must attain a second chronic phase * Acute myeloid leukemia, acute lymphoblastic leukemia, or myelodysplastic syndromes, meeting any of the following criteria: * Molecular relapse, as evidenced by \< 5% blasts in the bone marrow and the patient's leukemia-specific molecular abnormality detectable by PCR * Cytogenetic relapse, as evidenced by \< 5% blasts in the bone marrow and the patient's leukemia-specific chromosome abnormality detectable by standard cytogenetics at any time after day 60 post-transplant * Hematologic relapse, as evidenced by \> 20% blasts in bone marrow or soft tissue recurrence * Must be treated with chemotherapy after transplant, but before study donor lymphocyte infusion (DLI) * Multiple myeloma * Relapsed disease or recurrence of M-protein after thalidomide or other salvage treatment * Prior post-transplant documentation of disappearance of M-protein by immunofixation * Residual or progressive disease * Rising M-protein level at any time post-transplant (measured at 3-month intervals) * Original M-protein detectable at 6 months post-transplant * Immune protein electrophoresis (IPEP) is required to show that M-component is the same on day 60 post-transplant as pre-transplant * Residual (\> 5%) plasma cells in bone marrow * Relapsed non-Hodgkin lymphoma or Hodgkin lymphoma * Relapse or progression of disease must be evidenced within 3 months prior to donor lymphocyte infusion by physical exam, radiographic studies, or molecular studies * Tumor should be re-biopsied to determine histology * If Epstein-Barr virus (EBV) lymphoma is suspected, peripheral blood must be assayed for EBV genome (i.e., EBV DNA testing by PCR) within the past 30 days * EBV infection with associated pancytopenia * Persistent or refractory pancytopenia with EBV genome detected by PCR in the peripheral blood * Refractory pancytopenia is defined as pancytopenia that is poorly responsive to growth factors and/or transfusions * EBV lymphoproliferative disorder * Clonal lymphadenopathy that is refractory to standard therapy with acyclovir and immunoglobulin (DLI may be given with rituximab) * Not a candidate for repeat ASCT * Chimerism status is not required for determining eligibility for DLI * Patients eligible for allogeneic ASCT, but for whom DLI is offered as the first option, should have full donor chimerism at relapse or after therapy for relapsed disease * Patients with relapsed underlying disease after transplant who achieved remission after chemotherapy are allowed * No CNS recurrence that is not cleared by standard chemotherapy * CNS remission status must be maintained for 2 weeks * Original hematopoietic progenitor stem cell donor must be available for cell donation * No syngeneic donors PATIENT CHARACTERISTICS: * Karnofsky performance status 60-100% * Life expectancy ≥ 8 weeks * Creatinine \< 3 mg/dL * ABO/Rh and CMV IgG/IgM status known * No HIV1 and HIV2 antibody * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months (males) or 6 months (females) after completion of study treatment PRIOR CONCURRENT THERAPY: * See Disease Characteristics