Allogeneic or Haploidentical Stem Cell Transplant Followed By High-Dose Cyclophosphamide in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * AML without complete remission (CR/CRc/CRi) after at least 2 induction therapies OR * AML that has relapsed within 6 months after obtaining a CR OR * AML that has relapsed more than 6 months after obtaining a CR, and has treatment failure (TF) or progressive disease (PD) following at least 1 re-induction regimen OR * AML that has relapsed post Allogeneic transplantation * Active AML (bone marrow blasts ≥ 5% by morphology, staining, or flow) and/or presence of estramedullary disease * Available HLA-haploidentical donor that meets the following criteria: * Blood-related family member (sibling (full or half), offspring, or parent, cousin, niece or nephew, aunt or uncle, or grandparent) * At least 18 years of age * HLA-haploidentical donor/recipient match by at least low-resolution typing per institutional standards * In the investigator's opinion, is in general good health, and medically able to tolerate leukapheresis required for harvesting HSC * No active hepatitis * Negative for HTLV and HIV * Not pregnant NOTE: there were HLA-matched sibling and HLA-matched unrelated donor cohorts, but those closed without completion of accrual with Amendment 11 * Karnofsky performance status ≥ 50 % * Adequate organ function as defined below: * Total bilirubin ≤ 2.5 mg/dl (unless the patient has a history of Gilbert's syndrome) * AST(SGOT) and ALT(SGPT) ≤ 3.0 x IULN * Creatinine ≤ 2.0 x IULN OR estimated creatinine clearance ≥ 30 mL/min/1.73 m2 by Cockcroft-Gault Formula * Oxygen saturation ≥ 90% on room air * LVEF ≥ 40% * FEV1 and FVC ≥ 40% predicted, DLCOc ≥ 40% predicted. If DLCO is \< 40%, patients will still be considered eligible if deemed safe after a pulmonary evaluation. * At least 18 years of age at the time of study registration * Able to understand and willing to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable) Exclusion Criteria: * Circulating blast count ≥ 10,000/uL by morphology or flow cytometry (cytoreductive therapies including leukapheresis or hydroxyurea are allowed) * Known HIV or Active hepatitis B or C infection * Known hypersensitivity to one or more of the study agents * Currently receiving or has received any investigational drugs within the 14 days prior to the first dose of study drug (Day -7) * Currently receiving or has received any intensive chemotherapy within the 14 days prior to the first dose of study drug (Day -7) (hydrea or other non-intensive regimens such as decitabine may be used but must stop at least one day prior to the first dose of study drug) * Pregnant and/or breastfeeding * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, unstable cardiac arrhythmias, or psychiatric illness/social situations that would limit compliance with study requirements.