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