Inclusion Criteria:

          -  Acute lymphoblastic leukemia

               -  ≥ Complete remission 2 (CR2) (adults ≥ 18 years and ≤ 55 years)

               -  CR2 in pediatrics (defined as <18 years) and <12 months duration of first
                  remission

               -  ≥ CR3 or not in remission (pediatric patients <18 years)

               -  T cell leukemia ≥ CR2

               -  Evidence of pre-transplant minimal residual disease (MRD) by flow cytometry, FISH
                  or cytogenetics

          -  Myelodysplastic syndrome

               -  ≤ 55 years of age and ≥ 10% blasts, not responsive to hypomethylating agents
                  and/or conventional therapy

          -  Acute myeloid leukemia

               -  Not in remission (pediatric patients <18 years)

               -  Not in remission (10-30% blasts in the bone marrow for adult patients ≥18 years
                  and ≤ 55 years)

               -  Evidence of pre-transplant minimal residual disease (MRD) by flow cytometry, FISH
                  or cytogenetics

          -  Multiple myeloma

               -  No prior autologous transplant and fitting into one of the following disease
                  categories:

                    -  Early disease stage (CR1/PR1) with high-risk molecular features

                    -  Early disease stage (CR1/PR1) with high-risk clinical features

                    -  Late disease stage (CR2/PR2+) with high-risk clinical features

          -  Other high risk hematologic malignancies - to be approved by 2 or more
             hematology/oncology and BMT physicians

          -  Patients with prior CNS involvement are eligible provided that it has been treated and
             is in remission. CNS therapy (chemotherapy or radiation) should continue as medically
             indicated during the protocol.

          -  Have acceptable organ function within 14 days of study registration defined as:

               -  Renal: glomerular filtration rate > 60ml/min/1.73m2

               -  Hepatic: bilirubin, aspartate aminotransferase (AST), alanine aminotransferase
                  (ALT), Alkaline phosphatase (ALP) < 5 x upper limit of normal (ULN)

               -  Pulmonary function: Carbon Monoxide Diffusing Capacity corrected (DLCOcorr) > 50%
                  of normal, (oxygen saturation [>92%] can be used in child where pulmonary
                  function tests (PFT's) cannot be obtained)

               -  Cardiac: left ventricular ejection fraction ≥ 45% by echocardiogram (ECHO) or
                  multi gated acquisition scan (MUGA)

          -  Karnofsky performance status (PS) >80% for ages 16 years and older or Lansky Play
             Score >50 for < 16 years

          -  An acceptable source of stem cells according to current University of Minnesota BMT
             program guidelines:

               -  UCB graft will be composed of two partially HLA matched units. Each unit must be
                  matched at 4-6 HLA loci to the recipient and to each other. If two matched units
                  are not available, then a single HLA 4-6 matched unit may be used if of adequate
                  cell dose - total graft dose must be >3 x 107 MNC/kg

               -  HLA-matched related donor (6/6 or 5/6 antigen match)

               -  HLA-matched unrelated adult donor (if previously identified)

          -  Women of childbearing potential must agree to use adequate contraception (diaphragm,
             birth control pills, injections, intrauterine device [IUD], surgical sterilization,
             subcutaneous implants, or abstinence, etc.) for the duration of treatment.

          -  Voluntary written consent

        Exclusion Criteria:

          -  Active uncontrolled infection at time of enrollment or documented fungal infection
             within 3 months.

          -  Evidence of Human immunodeficiency virus (HIV) infection

          -  Pregnant or breast feeding. The agents used in this study may be teratogenic to a
             fetus and there is no information on the excretion of agents into breast milk. All
             females of childbearing potential must have a blood test or urine study within 2 weeks
             prior to registration to rule out pregnancy.

          -  Prior myeloablative transplant within the last 6 months

          -  Prior total body irradiation (TBI) making total marrow irradiation (TMI) not feasible