DISEASE CHARACTERISTICS: Any of the following hematologic malignancies or bone marrow failure syndromes: Acute myelogenous leukemia after induction failure, in relapse, or in second or greater complete remission (CR) Acute lymphocytic leukemia after induction failure, in relapse, in second or greater CR, or in first CR with t(9;22), t(8;14), or t(4;11) Non-Hodgkin's lymphoma (intermediate or high grade) that has failed to achieve CR with at least 2 induction regimens, in relapse, or in second or greater CR Multiple myeloma with poor prognostic features (elevated beta-2 microglobulin or high labeling index) Hodgkin's disease in relapse or that failed to achieve CR after 2 chemotherapy regimens Congenital or acquired bone marrow failure that is poorly responsive to or intolerant of current therapy Myelodysplastic syndrome of all subtypes except refractory anemia No Fanconi's anemia Patients must have a haploidentical donor and meet the following criteria: Likely to have clinical deterioration and rapid disease progression during an unrelated donor search OR Already had an unproductive donor search OR Ineligible for or has refused autologous transplant Lack an HLA A, B, DR, and DQ matched related donor (evaluated via both genotype and phenotype) Lack an HLA A, B, and DR matched unrelated donor (evaluated via both genotype and phenotype) 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: 40 and under Performance status: ECOG 0-2 OR Lansky 50-100% for patients under 16 years Life expectancy: At least 12 weeks Hematopoietic: Blood differential count with greater than 25% blasts at time of leukapheresis Hepatic: ALT and AST no greater than 5.0 times upper limit of normal (ULN) Bilirubin no greater than 2 times ULN unless due to Gilbert's syndrome or hemolytic anemia Renal: Creatinine less than 2 times ULN Cardiovascular: Adequate cardiac function for age Pulmonary: Adequate pulmonary function for age Other: Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception for 1 month prior to study until at least 2 months after study No active uncontrolled infection HIV negative

PRIOR CONCURRENT THERAPY: Biologic therapy: No prior bone marrow transplant No other concurrent monoclonal antibody therapies or ex vivo T-cell depletion therapies Chemotherapy: See Disease Characteristics Endocrine therapy: Not specified Radiotherapy: Not specified Surgery: Not specified