DISEASE CHARACTERISTICS:

• Eligible for and co-enrolled on protocol UMN-2005LS036, for treatment of any of the following advanced hematologic malignancies:

  • Acute leukemia in remission by morphology (< 5% blasts in bone marrow with cellularity ≥ 15%), including any of the following:

    • Acute myeloid leukemia (AML) in second or greater complete remission (CR) OR high-risk AML in first CR (CR1), meeting 1 of the following criteria:

      • Preceding myelodysplastic syndromes (MDS)
      • High-risk cytogenetics such as those associated with MDS or complex karyotype
      • Required more than 2 courses to obtain CR
      • Erythroblastic and megakaryocytic

    • Acute lymphoblastic leukemia/lymphoma in second or greater CR OR high-risk disease in CR1, meeting 1 of the following criteria:

      • High-risk cytogenetics (e.g., t[9:22], t[1;19], t[4;11], or other mixed-lineage leukemia rearrangements)
      • More than 1 course to achieve CR

  • Chronic myelogenous leukemia

    • Chronic phase patients must have failed or been intolerant to imatinib mesylate
    • No refractory blast crisis

  • Myelodysplastic syndromes (MDS)

    • Blasts must be < 5% (may achieve with induction therapy prior to transplant)
    • Any subtype including refractory anemia if severe pancytopenia, increased blasts, and/or complex cytogenetics (IPSS 1.5 and 2.0) present

  • Large cell lymphoma, Hodgkin lymphoma, or multiple myeloma meeting 1 of the following criteria:

    • Chemotherapy-sensitive disease that has failed therapy
    • Patient ineligible for autologous transplantation

  • Chronic lymphocytic leukemia/small lymphocytic lymphoma, marginal zone B-cell lymphoma, or follicular lymphoma that has progressed after at least 2 prior therapies

    • Patients with bulky disease should undergo debulking chemotherapy before transplantation
    • Refractory disease allowed provided disease is nonbulky and an estimated tumor doubling time is ≥ 1 month

  • Lymphoplasmacytic lymphoma, mantle cell lymphoma, or prolymphocytic leukemia

    • Must be chemotherapy-sensitive after initial therapy
  • Bone marrow failure syndromes (no Fanconi anemia)
  • Myeloproliferative syndromes

• Not scheduled to receive antithymocyte globulin during conditioning regimen on protocol UMN-2005LS036, due to 1 of the following prior therapies:

  • Prior autologous transplantation
  • At least 2 courses of multiagent chemotherapy or highly immunosuppressive therapy within the past 3 months

• Must be ineligible for autologous transplantation due to any of the following:

  • Prior autologous transplant
  • Inadequate autologous stem cell harvest
  • Inability to withstand a myeloablative preparative regimen
  • Clinically aggressive/high-risk disease

• Patients with stable disease are eligible provided the largest residual nodal mass is < 5 cm (approximately)

  • For patients who have responded to preceding therapy, the largest residual mass must represent a 50% reduction and be < 7.5 cm (approximately)

• No evidence of progressive disease by imaging modalities or biopsy

  • Persistent PET activity, though possibly related to lymphoma, is not an exclusion criteria in the absence of CT changes indicating progression
• No active CNS malignancy

• Must have two or three partially HLA-matched umbilical cord blood (UCB) units available

  • Units identified as the hematopoietic stem cell (HSC) source must be HLA-matched at 4-6 HLA-A and -B (at intermediate resolution) and -DRB1 (at high resolution) to the patient according to institutional guidelines
  • The UCB unit identified as the T-regulatory (Treg) cell source must be HLA-matched at 4-6 HLA antigens with the patient (without an HLA or ABO-matching criterion with the UCB units used as the HSC source)

  • Minimum cryopreserved cell dose of each unit is 1.5 x 10^7 nucleated cells/kilogram recipient body weight

    • If 2 UCB units are required to reach the target cell dose, the units must also be HLA-matched at 4-6 HLA- A, -B, and -DRB1 antigens with each other not necessarily at the same loci and they also must be ABO-matched to each other but not to the patient

PATIENT CHARACTERISTICS:

• Not requiring O_2

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• More than 12 months since prior autologous hematopoietic stem cell transplantation