Combination Chemotherapy Followed By Umbilical Cord Blood Transplantation in Treating Patients With Hematologic Cancer or Severe Aplastic Anemia

You may be eligible if

• DISEASE CHARACTERISTICS:
• One of the following histologically confirmed diagnoses:
• * Acquired severe aplastic anemia
• * Meets at least 2 of the following criteria:
• * Granulocyte count less than 500/mm\^3
• * Platelet count less than 20,000/mm\^3
• * Absolute reticulocyte count less than 20,000/mm\^3 (after correction for hematocrit)
• * Unresponsive to OR recurrent disease after prior treatment with anti-thymocyte globulin and/or cyclosporine
• * Acute myeloid leukemia (AML), meeting 1 of the following criteria:
• * Failed induction therapy
• * In first complete remission (CR) with any of the following high-risk features:
• * Stem cell or biphenotype classification (M0)
• * Erythroleukemia (M6)
• * Acute megakaryocytic leukemia (M7)
• * Cytogenetic markers indicative of poor prognosis
• * t(15;17) translocation and failed first-line induction therapy OR there is molecular evidence of persistent disease
• * t(8;21) and inv(16) translocations and failed first-line induction therapy
• * In early relapse\*
• * In second or subsequent remission
• * Recurrent disease after prior autologous stem cell transplantation (SCT) NOTE: \*No refractory relapse
• * Acute lymphoblastic leukemia, meeting 1 of the following criteria:
• * In early relapse\*
• * In second or subsequent remission
• * In first CR with the following high-risk features:
• * t(4;11) or t(9;22) translocation
• * Hyperleukocytosis (initial WBC greater than 30,000/mm\^3)
• * Failed to achieve CR by day 28 of standard induction therapy
• * Recurrent disease after prior autologous SCT NOTE: \*No refractory relapse
• * Chronic myelogenous leukemia
• * Chronic or accelerated phase that has failed medical management
• * Blastic phase allowed after reinduction chemotherapy induces chronic phase
• * Myelodysplastic syndromes meeting 1 of the following criteria:
• * Refractory to medical management
• * Presence of cytogenetic abnormalities predictive of transformation to acute leukemia, including the following:
• = 5q- = 7q-
• Monosomy 7 and trisomy 8
• Evidence of evolution to AML (e.g., refractory anemia with excess blasts \[RAEB\], or RAEB in transformation)
• * Chronic lymphocytic leukemia
• * Refractory to treatment including fludarabine-based therapy
• * Recurrent disease after prior autologous SCT
• * Multiple myeloma
• * Recurrent disease after prior autologous SCT
• * Beyond first CR or failed induction therapy
• * Disease is sensitive to pretransplantation cytoreduction
• * Hodgkin's lymphoma
• * Beyond first CR or failed induction therapy
• * Disease is sensitive to pretransplantation cytoreduction
• * Non-Hodgkin's lymphoma (NHL)
• * Recurrent disease after prior autologous SCT
• * Beyond first CR or failed induction therapy
• * Disease is sensitive to pretransplantation cytoreduction
• * Mantle zone NHL allowed after induction therapy
• * Myeloproliferative disorders
• * Refractory to medical management
• * Allografting required unless grade 3 or greater myelofibrosis by bone marrow biopsy
• * No HLA-matched sibling donor available
• * Ineligible for a myeloablative conditioning regimen due to advanced age (over 55), extensive prior therapy, and/or other comorbidities
• * If under age 55, must meet at least 1 of the following criteria:
• * Received extensive prior therapy
• * Organ toxicity or infection precluding eligibility for allogeneic transplantation with full ablation conditioning
• * Availability of 2-5 umbilical cord blood units that are at least a 4/6 HLA match
• * No active CNS disease
• * No primary or grade 3 or 4 myelofibrosis
• PATIENT CHARACTERISTICS:
• Age
• Any age
• Performance status
• Karnofsky 70-100% (for patients 16 years of age and older)
• Lansky 50-100% (for patients under 16 years of age)
• Life expectancy
• At least 3 months
• Hematopoietic
• See Disease Characteristics
• Hepatic
• ALT/AST less than 4 times normal
• Bilirubin less than 2.0 mg/dL (unless due to hepatic infiltration by primary malignancy)
• Renal
• Creatinine clearance greater than 40 mL/min
• Cardiovascular
• Shortening fraction or ejection fraction greater than 40% of normal value for age by echocardiogram or radionuclide scan
• Pulmonary
• FVC and FEV\_1 greater than 60% of predicted
• DLCO greater than 60% of predicted (adult patients)
• Clearance by pulmonologist required if patient cannot perform pulmonary function tests
• Other
• Not pregnant or nursing
• No uncontrolled active infection (viral, bacterial, or fungal)
• HIV negative
• PRIOR CONCURRENT THERAPY:
• Biologic therapy
• See Disease Characteristics
• More than 3 months since prior autologous stem cell transplantation
• Chemotherapy
• See Disease Characteristics
• At least 4 weeks since prior chemotherapy
• Endocrine therapy
• Not specified
• Radiotherapy
• Not specified
• Surgery
• Not specified
• Other
• Recovered from prior therapy
• No other concurrent investigational agents that would preclude study participation or increase risk to patient
• * Investigational diagnostic procedures allowed