Inclusion Criteria

DISEASE CHARACTERISTICS:

- Diagnosis of advanced hematologic malignancy or other disease not curable by
conventional chemotherapy, including any of the following:

- Acute myeloid leukemia in complete remission (CR)* (as defined by hematologic
recovery, < 5% blasts in the bone marrow by morphology, and a cellularity of >
15%), meeting one of the following criteria:

- In first complete remission (CR1) AND has high-risk disease as evidenced by
any of the following:

- Preceding myelodysplastic syndromes (MDS)

- High-risk cytogenetics (e.g., monosomy 5 or 7, or as defined by
referring institution treatment protocol)

- Required > 2 courses of therapy to obtain CR

- Erythroblastic or megakaryocytic leukemia

- In second CR (CR2) or beyond

- Acute lymphoblastic leukemia in CR* (as defined by hematologic recovery, < 5%
blasts in the bone marrow by morphology, and a cellularity of > 15%), meeting
one of the following criteria:

- In CR1 AND has high-risk disease as evidenced by any of the following:

- t(9;22), t(1;19), t(4;11), or other MLL rearrangements

- Hyplodiploid

- Required > 1 course of therapy to obtain CR

- Beyond CR2

- Chronic myelogenous leukemia (CML)

- All types are allowed (except refractory blast crisis CML)

- Patients in chronic phase CML must have failed or been intolerant to prior
imatinib mesylate (Gleevec) or other tyrosine kinase inhibitors

- MDS

- Any subtype allowed (including refractory anemia [RA])

- Severe pancytopenia or complex cytogenetics

- Blasts must be < 5% (if blasts are ≥ 5%, pre-transplant induction therapy
is required to reduce blast count to < 5%)

- Large cell lymphoma, Hodgkin lymphoma, or multiple myeloma, meeting one of the
following criteria:

- Chemotherapy-sensitive disease that has failed prior therapy

- Patients with large cell lymphoma or Hodgkin lymphoma must not have
progressive disease during salvage therapy (stable disease allowed
provided it is non-bulky)

- Ineligible for an autologous stem cell transplant

- Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone
B-cell lymphoma, or follicular lymphoma that has progressed after ≥ 2 prior
therapies

- Patients with bulky disease should be considered for debulking chemotherapy
prior to transplant

- Patients with refractory disease are eligible provided disease is non-bulky
AND an estimated tumor doubling time is ≥ 1 month

- Lymphoplasmacytic lymphoma, mantle cell lymphoma, or prolymphocytic leukemia

- Chemotherapy-sensitive disease that was previously treated with initial
therapy

- Patients with mantle cell lymphoma must not have progressive disease
during salvage therapy (stable disease allowed provided it is
non-bulky)

- Mycosis fungoides and Sezary syndrome

- Bone marrow failure syndromes, except for Fanconi anemia

- Myeloproliferative syndromes NOTE: *Patients for whom adequate marrow/biopsy
specimens can not be obtained to determine remission status by morphologic
assessment must have fulfilled criteria of remission (< 5% blasts by flow
cytometry and recovery of peripheral blood counts with no circulating blasts)

- Ineligible for autologous stem cell transplant due to any of the following:

- Prior autologous stem cell transplant

- Inadequate autologous stem cell harvest

- Inability to withstand a myeloablative preparative regimen

- Clinically aggressive/high-risk disease

- No evidence of progressive disease by imaging modalities or biopsy (persistent PET
scan activity allowed provided there are no CT scan changes indicating progression)

- Acute leukemia that is refractory, persistent, or relapsed (defined as > 5% blasts in
normocellular bone marrow) allowed provided patient was rendered aplastic either by
induction chemotherapy or radioimmunoconjugated monoclonal antibody therapy

- Patients with stable disease are eligible provided the largest residual nodal mass is
approximately < 5 cm (largest residual mass must represent a 50% reduction and be
approximately < 7.5 cm for patients who have responded to prior therapy)

- No active CNS malignancy

- Umbilical cord blood (UCB) donor available

- UCB graft matched at 4/6 HLA-A, -B, and -DRB1 antigens with the recipient

- May include 0-2 antigen mismatches at the A, B, or DRB1 loci

- Unit selection based on cryopreserved nucleated cell dose and HLA-A, -B,
and -DRB1 using intermediate resolution A, B antigen and DRB1 allele typing

- If 2 UCB units are required to reach the target cell dose, each unit must be a
3/6 HLA-A, -B, and -DRB1 antigen match to each other, as well as a 4/6 antigen
match to the recipient

- No 5-6/6 HLA-A, -B, and -DRB1 matched sibling donor available

PATIENT CHARACTERISTICS:

- Karnofsky performance status (PS) 60-100% OR Lansky PS 50-100%

- Creatinine ≤ 2.0 mg/dL (adults) OR creatinine clearance > 40 mL/min (pediatrics)

- Adult patients with a creatinine > 1.2 mg/dL or a history of renal dysfunction
must have an estimated creatinine clearance of > 40 mL/min

- Not pregnant or nursing

- Negative pregnancy test

- LVEF ≥ 35%

- DLCO > 30% predicted

- No requirement for O_2

- No decompensated congestive heart failure

- No uncontrolled arrhythmia

- None of the following liver diseases or conditions:

- Fulminant liver failure

- Cirrhosis with evidence of portal hypertension or bridging fibrosis

- Alcoholic hepatitis

- Esophageal varices

- History of bleeding esophageal varices, hepatic encephalopathy, or correctable
hepatic synthetic dysfunction as evidenced by prolongation of the prothrombin
time

- Ascites related to portal hypertension

- Bacterial or fungal abscess

- Biliary obstruction

- Chronic viral hepatitis with total serum bilirubin > 3 mg/dL

- Symptomatic biliary disease

- Recent mold infection (e.g., Aspergillus) allowed provided patient received ≥ 30 days
of appropriate treatment AND infection is controlled and cleared by Infectious
Disease

- No evidence of HIV infection or known HIV-positive serology

- No uncontrolled viral or bacterial infection

PRIOR CONCURRENT THERAPY:

- See Disease Characteristics

- At least 3 months since prior myeloablative stem cell transplantation