CD33-CAR T Cell Therapy for the Treatment of Recurrent or Refractory Acute Myeloid Leukemia

Inclusion Criteria: Documented informed consent of the participant and/or legally authorized representative Assent, when appropriate, will be obtained per institutional guidelines For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening, while the request for a translated full consent is processed Agreement to allow the use of archival tissue from diagnostic tumor biopsies If unavailable, exceptions may be granted with Study principal investigator (PI) approval Age: >= 18 years Karnofsky Performance Scale (KPS) >= 70 Life expectancy >= 16 weeks at the time of enrollment Prior allogeneic transplant allowed if > 6 months prior to study enrollment Participant must have a confirmed diagnosis of active CD33+ AML de novo, or secondary OR participants who are at a high risk for disease recurrence Relapsed AML is defined as patients that had a first complete response (CR) before developing recurrent disease (increased bone marrow blasts) Refractory AML is defined as patients that have not achieved a first CR after induction chemotherapy. For patients with AML evolving from myelodysplastic syndrome, they should have completed at least one cycle of induction chemotherapy Research participants must have bone marrow and/or peripheral blood samples available for confirmation of diagnosis of AML CD33 positivity must be confirmed by either flow cytometry or immunohistochemistry within 90 days of study entry. Cytogenetics, flow cytometry, and molecular studies (such as FLT-3 status) will be obtained as per standard practice Research participants who are at a high risk of disease recurrence, they must have historical bone marrow and/or peripheral blood samples available for confirmation of diagnosis of AML No known contraindications to lymphodepleting agents, steroids, tocilizumab and/or cetuximab, or the investigational agent Total serum bilirubin =< 2.0 mg/dL Participants with Gilbert syndrome may be included if their total bilirubin is =< 3.0 Aspartate aminotransferase (AST) =< 3 x the upper limit of normal (ULN) Alanine aminotransferase (ALT) =< 3 x ULN Estimated creatinine clearance of >= 60 mL/min per the Cockcroft-Gault formula, and the participant is not on hemodialysis Left ventricular ejection fraction >= 50% within 8 weeks before enrollment Oxygen (O2) saturation > 92% not requiring oxygen supplementation Women of childbearing potential (WOCBP): negative urine or serum pregnancy test If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for > 1 year (women only) Research participants must have a potential donor or stem cell source identified for allogeneic transplantation, either related (7/8 or 8/8 allele matched or haploidentical) DONOR: The identified donor must be the original donor whose stem cells were used for the research participant's allogeneic hematopoietic stem cell transplantation (alloSCT) DONOR: The donor must be HIV negative DONOR: KPS >= 70 DONOR: Documented body weight Exclusion Criteria: Prior allogeneic transplant if < 6 months prior to enrollment Concurrent use of systemic steroids or chronic use of immunosuppressant medications should be stopped 28-days prior to enrollment. Recent or current use of inhaled or topical steroids in standard doses is not exclusionary. Physiologic replacement of steroids (prednisone =< 7.5 mg/day, or equivalent doses of other corticosteroids) is allowed Participants with active autoimmune disease, including graft versus host disease (GvHD), requiring systemic immune suppressive should be stopped 28-days prior to enrollment Participants may not be receiving any other investigational agents and are not dependent on concurrent biological therapy, chemotherapy, or radiation therapy With exception to Hydrea which must be stopped prior to initiation of lymphodepletion Research participants on active systemic antifungal treatment within 8 weeks of enrollment are not eligible. However, participants on antifungal prophylaxis are eligible Not applicable at the time of enrollment if the research participant's donor is undergoing leukapheresis Subjects with >= Grade 2 myelofibrosis on bone marrow biopsy Subjects with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of screening if the patient is undergoing leukapheresis. Patients with controlled atrial arrythmia is allowed Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia History of stroke or intracranial hemorrhage within 6 months prior to screening Subjects with presence of other active malignancy, however, research participants with history of prior malignancy treated with curative intent and in complete remission are eligible Clinically significant uncontrolled illness Active infection requiring antibiotics Research participants who have tested human immunodeficiency virus (HIV) positive, or have active hepatitis B or C infection based on testing performed within 4 weeks of enrollment Active viral hepatitis Females only: Pregnant or breastfeeding Any other condition that would, in the Investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns with clinical study procedures Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)