DISEASE CHARACTERISTICS: Histologically proven Hodgkin's disease (HD), non-Hodgkin's lymphoma (NHL), and multiple myeloma (MM) meeting the following requirements: Refractory to or at high risk following prior therapy Responded with at least a partial response to last cytoreductive regimen No bulky disease (individual tumor diameter larger than 5 cm) Eligible HD: CNS involvement at original presentation and currently in complete response (CR) Relapsed within 1 year following completion of front-line MOPP or ABVD Relapsed at any time following front-line MOPP/ABVD or other hybrid Eligible NHL: Any grade lymphoma with CNS involvement at original presentation and currently in CR High-grade lymphomas (International Working Formulation H-J) with marrow involvement at original presentation and currently in CR, EXCEPT: Immunoblastic lymphoma and large cell (IWF G and H) with bone marrow involvement with small cleaved cell at original presentation High-/intermediate-grade lymphomas (IWF D-J) in relapse after adequate front-line therapy High-/intermediate-grade lymphomas (IWF D-J) that failed to achieve CR with adequate front-line therapy Low-grade lymphomas (IWF A-C) with B symptoms at original presentation and relapse after front-line therapy Low-grade lymphomas (IWF A-C) in relapse within 1 year following last chemotherapy Low-grade lymphomas (IWF A-C) with documented histologic conversion Eligible MM: Diagnosis based on either presence of both Group I diagnostic criteria OR One Group I criterion and all Group II criteria Group I diagnostic criteria: Plasma cells and/or myeloma cells greater than 10% in bone marrow Biopsy-proven plasmacytoma in bone or soft tissue Group II diagnostic criteria: Monoclonal serum protein spike Urinary myeloma protein Osteolytic lesions on radiologic examination Generalized osteoporosis suffices if plasma cells in marrow exceed 30% Myeloma cells in at least 2 peripheral blood smears Stage II/III disease documented sometime during clinical course Stage III defined by presence of at least 1 of the following: Hemoglobin less than 8.5 g/dl Serum calcium greater than 12 mg/dl Advanced lytic bone lesions High M-component production rates: IgG greater than 7 g/dl IgA greater than 5 g/dl Urinary light chain greater than 4 g/24 hours Stage II disease defined by absence of Stage III characteristics but presence of at least 1 of the following: Hb less than 10 g/dl More than 1 osteolytic lesion, none advanced IgG greater than 5 g/dl IgA greater than 3 g/dl Bone marrow donor available for lymphoma patients with marrow involvement Perfosfamide-purged autologous transplant allowed in patients with no matched sibling donor if: Marrow involvement is limited (less than 30% tumor cells on smears and in bilateral iliac crest biopsies) AND Age is under 60 Donor requirements: Excellent physical condition by history, lab studies, PE No physiologic, psychologic, or medical inability to tolerate the procedure No increased anesthetic risk No HIV infection Priority of multiple donors (in order given): ABO compatible Age over 18 Same sex as recipient 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.