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

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