RATIONALE: Monoclonal antibodies such as daclizumab can locate tumor cells and either kill them or deliver tumor-killing substances to them without harming normal cells. Peripheral stem cell transplantation from a brother or sister may be effective treatment for hematologic cancer. Sometimes the transplanted cells can be rejected by the body's tissue. Mycophenolate mofetil, tacrolimus, and donor white blood cells may prevent this from happening.

PURPOSE: Phase II trial to study the effectiveness of mycophenolate mofetil, tacrolimus, daclizumab, and donor peripheral stem cell transplantation in treating patients who have hematologic cancer.

OBJECTIVES: I. Determine whether donor hematopoiesis can be safely established using a nonmyeloablative conditioning regimen followed by HLA matched sibling donor peripheral blood stem cell transplantation in patients with hematologic malignancies. II. Determine whether mixed chimerism can be safely converted to full donor hematopoiesis with this treatment regimen in these patients. III. Determine the toxicity and incidence of aplasia and graft versus host disease in these patients treated with this regimen. IV. Determine the antitumor potential of this treatment regimen in these patients. V. Determine the role of NFkB in the modulation of the cytokine secretion profile of T lymphocytes during an alloimmune response in these patients treated with this regimen.

OUTLINE: Patients receive immunosuppressive medications consisting of oral mycophenolate mofetil and tacrolimus twice a day beginning on day -8 and continuing through day 45 (in the absence of graft versus host disease). Patients also receive daclizumab IV over 30 minutes on days -1, 3, and 8. Patients undergo allogeneic peripheral blood stem cell (PBSC) transplantation with donor CD34+ cells IV on day 0. If there is 0-80% donor hematopoiesis, patients receive donor lymphocyte infusions with CD3+ cells IV on days 75, 165, and 270.

PROJECTED ACCRUAL: A total of 10-45 patients will be accrued for this study.

DISEASE CHARACTERISTICS: Diagnosis of any of the following hematologic malignancies: Multiple myeloma Non-Hodgkin's lymphoma Indolent OR Relapsed or primary refractory high grade or intermediate grade in complete remission (CR) or partial remission (PR) after salvage chemotherapy or autologous bone marrow transplantation Hodgkin's disease Relapsed or primary refractory in CR or PR after salvage chemotherapy or autologous bone marrow transplantation Chronic lymphocytic leukemia Chronic myeloid leukemia Myelodysplastic syndrome Acute myeloid leukemia with high risk CR1 or second or greater CR Acute lymphocytic leukemia with high risk CR1 or second or greater CR Must have a 6 antigen HLA identical sibling donor Must have one of the following conditions that confer an increased risk for undergoing allogeneic bone marrow transplantation after myeloablative preparative regimen: Over 55 years of age AST or ALT greater than 2.5 times upper limit of normal (ULN) Bilirubin greater than 1.8 times ULN Renal dysfunction with creatinine greater than 1.5 mg/dL (after 12 courses of prior cytotoxic therapy) Undergone one or more prior autologous bone marrow transplantations Refuse to undergo allogeneic bone marrow transplantation using a myeloablative preparative regimen A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology.

PATIENT CHARACTERISTICS: Age: Over 18 Performance status: ECOG 0-2 Life expectancy: Not specified Hematopoietic: Not specified Hepatic: See Disease Characteristics Renal: See Disease Characteristics Other: Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY: Biologic therapy: See Disease Characteristics Chemotherapy: See Disease Characteristics Endocrine therapy: Not specified Radiotherapy: Not specified Surgery: Not specified