Inclusion Criteria:

• Age < or equal to 55
• Availability of donor cord blood (one to three units) matching at least 4 of 6 HLA antigens (A, B, and DR). HLA class I antigens will be determined by serologic methods, and Class II antigens will be determined by high-resolution DNA typing. Typing will be confirmed by UCSF Immunogenetics Department following infusion. The UCB units must contain >2.5 x 10(7) TNC per kilogram recipient body weight. Cord blood units will be obtained from all available international banks.
• HLA identical or 1 antigen mismatched related donors or potential HLA-matched unrelated donors (MUD) matching at >6/8 (A, B,C, DR) alleles must NOT be available.

• Disease types:

  • Acute myeloid leukemia not expected to be curable with chemotherapy. This will include patients with high-risk cytogenetics (-7, -7q, -5, -5q, t(6,9), t(9,11), complex, Ph+), evolution from prior myelodysplasia or AML secondary to prior chemotherapy, failure to achieve remission, or second or subsequent remission. To ensure adequate time until disease progression, marrow blasts must be < or equal to 10%. This may be achieved using chemotherapy treatment.
  • Myelodysplasia with high-risk features. This will include patients with IPSS category INT2 or HI-risk MDS. Marrow blasts must be < or equal to 20%. If required, chemotherapy may be given to achieve target levels of blasts.
  • Acute lymphoblastic leukemia not expected to be curable with chemotherapy. This will include patients with high-risk cytogenetics (Ph+, t(4,11), 11q23 abnormalities, and monosomy 7), patients requiring more than one induction course to achieve remission, as well as patients failing to enter remission or in second or subsequent remission. To ensure adequate time until disease progression, marrow blasts must be < or equal to 10%. If required, chemotherapy may be given to achieve target levels of blasts.
  • Chronic myelogenous leukemia with advanced disease. This will include patients with accelerated or blastic phase or patients with chronic phase refractory to STI-5741. To ensure adequate time until disease progression, patients with blast crisis must show marrow blasts < or equal to 10%. If required, chemotherapy may be given to achieve target levels of blasts.
  • Multiple myeloma, stage II-III with >1st relapse or refractory disease or newly diagnosed with chromosome 13 abnormalities.
  • Lymphoma: diffuse large cell, mantle cell, peripheral T-cell, T-NK cell, or Hodgkin's disease which has failed to respond to primary therapy, progressed or recurred after prior therapy. Patients who have failed autologous transplant are eligible if they are >1 year post-transplant.
• Patients must have an ECOG PS< or equal to 2
• Laboratory requirements:
• Creatinine <2.0mg/dL and creatinine clearance >40/m/min (calculated or based on 24 hour urine collection)
• Bilirubin <2.0 mg/dL, AST/alkaline phosphatase <3x upper limit of normal
• Patients with hepatitis C and active Hepatitis B are eligible only if a liver biopsy is performed and there is a < or equal to grade 2 inflammation or fibrosis.
• Cardiac ejection fraction >40%
• DLCO >40%
• Negative pregnancy test (females of reproductive age)

Exclusion Criteria:

• Active infection requiring ongoing antibiotic treatment
• HIV infection
• Poor performance status (ECOG >2)
• Rapid progression of malignant disease
• Opinion of BMT Committee that autologous transplant would be a preferable form of treatment
• Organ function is below requirements
• Pregnancy or breast-feeding