Inclusion Criteria

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