Inclusion Criteria:

          -  Patients must meet one of two disease criteria:

               -  Acute myelogenous leukemia (AML) within one of the following categories:

                    -  Primary induction failure (PIF): patients who have not achieved a complete
                       remission following initial diagnosis and after at least two induction
                       cycles of chemotherapy consisting of cytarabine and an anthracycline or
                       high-dose cytarabine

                    -  Relapsed AML: Patients are defined as having relapsed disease if they
                       entered a complete remission confirmed with a bone marrow biopsy following
                       initial treatment, and then were found to have morphological or cytogenetic
                       evidence of recurrent disease on a subsequent bone marrow exam

                    -  Any complete remission (CR) 2 or greater: CR must be defined using a bone
                       marrow exam taken at least 21 days since the last chemotherapy (including a
                       methyltransferase inhibitor), and may include CRp (morphologic CR without
                       peripheral platelet recovery)

                    -  CR1 with high-risk features: includes patients with treatment-related AML,
                       secondary AML (following myelodysplastic syndrome (MDS) or
                       myeloproliferative neoplasms (MPN)), high-risk cytogenetic or molecular
                       phenotype (by National Comprehensive Cancer Network (NCCN) criteria)

                    -  Untreated AML (> 20% blasts on a bone marrow) arising from a previous
                       confirmed diagnosis of MDS or MPN (excluding BCR-ABL (a genetic mutation)
                       positive diseases).

               -  Myelodysplastic syndromes within one of the following categories:

                    -  High-risk myelodysplastic syndrome (MDS) at diagnosis as defined by the
                       International Prognostic Scoring System (IPSS) or World Health Organization
                       (WHO) classification based Prognostic Scoring System (WPSS)

                    -  Transfusion dependent MDS (either red blood cells (RBC) or platelet
                       dependent) without a hematologic response to at least 4 months of
                       methyltransferase inhibitor (MTI) therapy; hematological response is defined
                       as transfusion independence for two or more months

                    -  Progressive MDS following at least 4 months of MTI therapy; progression is
                       defined as resumption of transfusion dependence after at least two months of
                       transfusion independence OR increase of marrow blasts by 50% from
                       pretreatment OR overall blasts over 10% of marrow cells at any time after
                       treatment

          -  Available related donor that is at least an allele level haplotype-match at human
             leukocyte antigen (HLA)- A, B, C, DP Beta 1 (DRB1) and DPB1 loci (DPB1 matching
             according to the "permissive - non-permissive" dichotomy as stated by University of
             Wisconsin (UW) Histocompatibility Laboratory); a minimum match of 5/10 loci is
             required; an unrelated donor search is not required for a patient to be eligible for
             this protocol

          -  Karnofsky score of 60% or better (requires occasional assistance, but is able to care
             for most of his/her needs)

          -  Diffusing capacity of the lungs for carbon monoxide (DLCO) (corrected for hemoglobin >
             40%; and forced expiratory volume in one second (FEV1) > 50%

          -  Ejection fraction (EF) >= 50% and no uncontrolled angina, symptomatic ventricular
             arrhythmias, or electrocardiogram (ECG) evidence of active ischemia

          -  Serum creatinine within normal range for age, or if serum creatinine outside normal
             range, then renal function (estimated glomerular filtration rate (GFR) by modification
             of diet in renal disease (MDRD) formula) > 40 mL/min/1.73 m^2

          -  Women of child bearing potential must have a negative pregnancy test within 14 days
             prior to study registration and agree to use adequate birth control during study
             treatment

          -  Voluntary written consent

          -  Patients must be 28 days from the end of the last induction course or at least 14 days
             from completion of previous methyltransferase inhibitor therapy (azacitidine or
             decitabine) at the time of registration

          -  DONOR: Donors must be at least HLA-haploidentical first degree relatives of the
             patients; eligible donors include biological parents, siblings, half-siblings or
             children

          -  DONOR: Age >= 18 years and =< 60 years

          -  DONOR: Donors must meet the selection criteria prior to the start of the recipient's
             pre-transplant conditioning regimen as defined by the Foundation for the Accreditation
             of Cell Therapy (FACT) and will be screened according to the American Association of
             Blood Banks (AABB) guidelines and UW Bone Marrow Transplant (BMT) program standard
             operating procedure (SOP)

        Exclusion Criteria:

          -  Active central nervous system (CNS) leukemia within two weeks of registration;
             patients with a history of CNS leukemia must have adequate treatment as defined by at
             least two negative spinal fluid assessments separated by at least one week; patients
             who have received cranial radiation therapy (XRT) must still be eligible to receive
             total body irradiation to 4 Gy

          -  New or active infection as determined by fever, unexplained pulmonary infiltrate or
             sinusitis on radiographic assessment; infections diagnosed within 4 weeks of
             registration must be determined to be controlled or resolving prior to treatment

          -  Active human immunodeficiency virus (HIV), hepatitis A, B or C infection

          -  Allergy or hypersensitivity to agents used within the treatment protocol

          -  DONOR: Recipient derived anti-donor high-titer (> 3000 MFI) HLA antibody as determined
             by Luminex assay

          -  DONOR: Not suitable for donation according to UW BMT program donor selection SOP