Inclusion Criteria:

   1. Eligible diseases include:

   A. Acute Lymphoblastic Leukemia (B- or T-ALL)

      1. Complete Response (CR)1-ultra high risk features

         - Unfavorable cytogenetics

         - Hypodiploidy

         - Induction failure

         - Minimal Residual Disease (MRD) positive after consolidation

      2. CR-2:

         - Any of the high risk features listed in CR1

         - B-ALL: any relapse considered eligible for transplant

         - T- ALL

      3. CR-3-any

   B. Acute Myeloid Leukemia

      1. MRD >5% at day 22 induction 1

      2. MRD >0.1% after induction 2

      3. FLT/ITD with allelic ratio > 0.4 and MRD >0.1% at day 22 or 29 induction 1

      4. Translocation (6:9), (8:6), (16:21), monosomy 7, monosomy 5, 5q

      5. M7 with KMT2A rearrangements, inv(16)(p13.3q24.3) [CBFA2T3-GLIS2] or
      t(11;12)(p15;p13) [NUP98-KDM5A]

      6. AML in 2nd or subsequent CR

      7. Therapy related or Secondary AML

      8. Refractory anemia with excess blasts (RAEB)2

   C. Myelodysplastic syndrome D. Mixed Phenotype Acute Leukemia MRD>1% after
   consolidation E. Non-Hodgkin's lymphoma (NHL) or Hodgkin's lymphoma (HL) beyond first
   remission

   2. Age ≥3 to ≤45 years old. Subjects 1 and 2 (in Cohort 1) will be ≥ 12 years old

   3. Available mismatched related donor (mMRD) or mismatched unrelated donor (mMUD), Human
   leukocyte antigen (HLA) matched 8/10 or 9/10

   4. Lansky (age <16) or Karnofsky (age ≥16) performance status ≥80%

   5. Able and willing to provide written, signed informed consent (assent as appropriate)

   6. Have adequate organ function defined as the following:

      - Serum Creatinine <1.5 X upper limit of normal (ULN) or 24-hour creatinine
      clearance >50 ml/min

      - Serum bilirubin ≤ 2 x ULN

      - Alanine aminotransferase (ALT) or aspartate aminotransferase (AST)

      ≤10 x ULN

      - Diffusion Capacity of the Lungs (DLCO) >60% predicted (in children, O2 saturation
      >92% on room air)

      - Left ventricular ejection fraction >45% (in children, shortening fraction >26%)

   7. Male and female subjects of child bearing potential must agree to use an effective
   method of birth control to avoid pregnancy throughout the transplant procedure, while
   on immunosuppression, and if the subject experiences any chronic GvHD.

Exclusion Criteria:

   1. Prior bone marrow or peripheral blood HSCT within the last 6 (six) months

   2. HLA-matched related or unrelated donor available

   3. Any active, uncontrolled infection at the time of enrollment

   4. Pregnant or lactating females

   5. Any severe concurrent disease which, in the judgement of the investigator, would place
   the patient at increased risk during participation in the study

   6. Any subject with a history of significant renal, hepatic, pulmonary, or cardiac
   dysfunction or on treatment to support cardiac dysfunction

   7. HIV positive

   8. Non-cooperative behavior or non-compliance of the patient and/or of his/her family

   9. Received another investigational agent within 30 days of enrollment

10. Patients with Down's syndrome