RATIONALE: Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. Combining chemotherapy with peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more cancer cells. Sometimes the transplanted cells are rejected by the body's normal tissues. Antithymocyte globulin may prevent this from happening.

PURPOSE: Phase II trial to study the effectiveness of chemotherapy plus biological therapy followed by peripheral stem cell transplantation in treating patients who have hematologic cancer.

OBJECTIVES: I. Determine the effect of nonmyeloablative chemotherapy followed by allogeneic peripheral blood stem cell transplantation on hematopoietic recovery in patients with hematologic malignancies. II. Determine the toxicities of this regimen in these patients. III. Determine the frequency of mixed hematopoietic chimerism in these patients after this therapy. IV. Determine the efficacy and toxicity of donor leukocyte infusions at relapse in these patients. V. Determine the response rates and survival of these patients after this therapy. VI. Determine the immune reconstitution of patients undergoing this therapy.

OUTLINE: Patients receive fludarabine IV over 30 minutes on days -9 to -5, cyclophosphamide IV over 1 hour on day -5, and antithymocyte globulin IV over 10 hours on days -5 to -2. Allogeneic peripheral blood stem cells are infused on day 0. Patients who achieve complete remission (CR) and then relapse or patients who achieve less than a CR before day 60 receive donor leukocyte infusions (DLI) over 30 minutes. DLI are repeated as necessary for persistent disease. Patients are followed at 1, 3, and 6 months, then at 1 and 2 years.

PROJECTED ACCRUAL: A total of 40 patients will be accrued for this study within 2 years.

DISEASE CHARACTERISTICS: Histologically proven hematologic malignancy for which there is no standard curative therapy, including, but not limited to: Low grade non-Hodgkin's lymphoma (NHL) Mantle cell lymphoma Chronic lymphocytic leukemia (stage II-IV) Myelodysplastic syndrome, including: Refractory anemia (RA) with ringed sideroblasts RA with excess blasts (RAEB) RAEB in transformation Chronic myelomonocytic leukemia Multiple myeloma OR Histologically proven hematologic malignancy that has failed 1 prior therapy OR is at high risk for relapse, including, but not limited to: Intermediate grade NHL High grade NHL Hodgkin's disease Acute lymphoblastic lymphoma Acute myelogenous leukemia OR Histologically proven chronic myelogenous leukemia in chronic or accelerated phase, with the following risk factors that preclude eligibility for standard allogeneic peripheral blood stem cell transplantation: Older age Poor performance status Healthy, partially related HLA 5/6 or 6/6 serologic match donor available 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: 18 to 60 or physiologic 70 Performance status: Karnofsky 0-2 Life expectancy: Not specified Hematopoietic: Not specified Hepatic: Bilirubin less than 2.0 mg/dL SGOT and SGPT less than 2 times normal No active hepatitis Renal: Creatinine less than 2.0 mg/dL OR Creatinine clearance greater than 50 mL/min Cardiovascular: Ejection fraction greater than 45% OR Cardiac clearance Pulmonary: DLCO at least 50% predicted Other: No active infection HIV-1, HIV-2, and HTLV-1 negative Not pregnant or nursing

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