Inclusion Criteria:

          -  Eligibility for pediatric patients will be determined in conjunction with an MD
             Anderson Cancer Center (MDACC) pediatrician; patients age 2-17 years old may be
             enrolled after at least 4 adults (ages 18-65 years old) have been treated without
             toxicity

          -  Patient with no matched related donor who has a related haploidentical donor
             identified (=< 7/8 allele match at the A, B, C, DR loci) who is willing to undergo a
             bone marrow harvest and an NK cell collection approximately 2 weeks of the recipient's
             admission for transplant; the donor must be 16 years of age or older and weigh at
             least 110 pounds

          -  Patients with one of the following diseases: acute myeloid leukemia (AML): a. first
             complete remission with high-risk features defined as: (i) greater than 1 cycle of
             induction therapy required to achieve remission; (ii) preceding myelodysplastic
             syndrome (MDS); (iii) presence of FLT3 mutations or internal tandem duplication or
             other mutations associated with poor-risk AML (e.g. DNMT3A, TET2); (iv)
             French-American-British Classification (FAB) M6 or M7 classification; (v) adverse
             cytogenetics: -5, deletion (del) 5q, -7, del7q, abnormalities involving 3q, 9q, 11q,
             20q, 21q, 17, +8 or complex karyotype (> 3 abnormalities); (vi) treatment-related AML,
             or b. second or greater remission; patients beyond second remission have to be in
             complete remission (CR) at transplant to be eligible, or c. primary induction failure
             with partial response to therapy who achieve adequate cytoreduction

          -  Patients with myelodysplastic syndromes (MDS): a. de novo MDS with intermediate or
             high-risk International Prognostic Scoring System (IPSS) scores; patients with
             intermediate-1 features should have failed to respond to hypomethylating agent
             therapy, or b. patients with treatment-related MDS

          -  Chronic myeloid leukemia (CML): a. failed to achieve cytogenetic remission or have
             cytogenetic relapse after treatment with at least 2 tyrosine kinase inhibitors, or b.
             accelerated phase or blast phase at any time

          -  Performance score of at least 70% by Karnofsky or 0 to 1 by Eastern Cooperative
             Oncology Group (ECOG) (age >= 12 years), or Lansky Play-performance scale of at least
             70% or greater (age < 12 years)

          -  Serum creatinine clearance equal or more than 50 ml/min (calculated with
             Cockcroft-Gault formula)

          -  Bilirubin equal or less than 1.5 mg/dl except for Gilbert's disease

          -  Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) equal or less than
             200 IU/ml for adults

          -  Conjugated (direct) bilirubin less than 2 x upper limit of normal

          -  Left ventricular ejection fraction equal or greater than 40%

          -  Diffusing capacity of the lung for carbon monoxide (DLCO) equal or greater than 50%
             predicted corrected for hemoglobin; for children =< 7 years of age who are unable to
             perform pulmonary function tests (PFT), oxygen saturation >= 92% on room air by pulse
             oximetry

          -  Patient or patient's legal representative, parent(s) or guardian should provide
             written informed consent; assent of a minor if participant's age is at least seven and
             less than eighteen years

        Exclusion Criteria:

          -  Human immunodeficiency virus (HIV) positive; active hepatitis B or C

          -  Uncontrolled infections; principal investigator (PI) is the final arbiter of this
             criterion

          -  Liver cirrhosis

          -  Central nervous system (CNS) involvement within 3 months

          -  Positive pregnancy test in a woman with child bearing potential defined as not
             post-menopausal for 12 months or no previous surgical sterilization

          -  Inability to comply with medical therapy or follow-up