Bone Marrow Transplantation With Specially Treated Bone Marrow in Treating Patients With Hematologic Cancer That Have Not Responded to Previous Therapy

Inclusion Criteria: * Age ≤40 years. * Diagnoses-patients with the following hematologic malignancies and bone marrow failure syndromes: * Acute myelogenous leukemia-induction failure, relapse, second or greater complete remission (CR) * Acute lymphocytic leukemia-induction failure, relapse, second or greater CR, first CR with t(9;22), t(8;14), or t(4;11) * Non-Hodgkin's lymphoma (intermediate or high grade) which has failed to achieve CR with at least two induction regimens, relapse, second or greater CR * Multiple myeloma with poor prognostic features (elevated 0-2 microglobulin or high labeling index) * Hodgkin's disease in relapse or which fails to achieve CR after two chemotherapy regimens * Congenital or acquired bone marrow failure - poorly responsive to or intolerant of current therapy * Myelodysplastic syndrome of all subtypes except refractory anemia (RA) * Patient has a haploidentical family member that meets medical criteria for donation. * Eligibility for other transplant types: * Patient considered likely to have clinical deterioration and rapid disease progression during an unrelated donor search, or * Patient who has already had an unproductive donor search or * Patient ineligible for or has refused autologous transplant * Adequate renal and hepatic function for age: * Serum creatinine \<2 x ULN * Alanine aminotransferase (ALT, SGPT) x ULN * Aspartate aminotransferase (AST, SGOT) x ULN * Total bilirubin 5\_2 x ULN except if bili…