Study of Adoptive Cellular Therapy Using Autologous T Cells Transduced With Lentivirus to Express a CD33 Specific Chimeric Antigen Receptor in Patients With Relapsed or Refractory CD33-Positive Acute Myeloid Leukemia

Inclusion Criteria: 1. Age 1-80 years of age. The pediatric cohort is defined as age younger than 18 years. 2. Patients with active (blood or bone marrow blasts \>5%) relapsed or refractory CD33+ acute myeloid leukemia (AML) de novo, or secondary. a. Relapsed AML is defined as patients that had a first complete remission (CR) before developing recurrent disease. b. Refractory AML defined as patients that have not achieved a CR after 2 cycles of induction chemotherapy. 3. Patients must have bone marrow and peripheral blood studies available for confirmation of diagnosis of AML; CD33 positivity must be confirmed by either flow cytometry or immunohistochemistry; cytogenetics, flow cytometry, and molecular studies (such as FMS-like tyrosine kinase-3 \[Flt-3\] status) will be obtained as per standard practice. 4. ECOG performance status score \</= 2. 5. Pretreatment calculated or measured creatinine clearance (absolute value) of \>= 60 mL/minute. 6. Serum bilirubin =\< 3.0 mg/dL. 7. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 5 times the institutional upper limits of normal. 8. Ejection fraction measured by echocardiogram (ECHO) or multi gated acquisition scan (MUGA) \>50%. 9. Subject does not require supplemental oxygen or mechanical ventilation, and oxygen saturation by pulse oximetry is 94% or higher on room air. 10. Negative serum pregnancy test. 11. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately. 12. Patients who have undergone allo-SCT are eligible if they are at least 3 months post SCT, have relapsed AML, are not on treatment or prophylaxis for GVHD, and have no active GVHD. 13. All patients or legally responsible parent or guardian must have the ability to understand and willingness to sign a written informed consent Exclusion Criteria: 1. Diagnosis of acute promyelocytic leukemia (APL M3): t(15;17)(q22;q12); (promyelocytic leukemia \[PML\]/retinoic acid receptor \[RAR\] alpha \[a\]) and variants excluded. 2. Patients with extramedullary disease as their sole site of relapsed AML. 3. Acceptable allogeneic stem cell donor with imminent plans to proceed with allo-SCT. 4. Known central nervous system (CNS) leukemic involvement that is refractory to intrathecal chemotherapy and/or cranio-spinal radiation; patients with a history of CNS disease that have been effectively treated to complete remission (\< 5 white blood cell \[WBC\]/mm\^3 and no blasts in cerebrospinal fluid \[CSF\]) will be eligible. 5. Ongoing or active or uncontrolled infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, poorly controlled pulmonary disease or psychiatric illness/social situations that would limit compliance with study requirements. 6. Human immunodeficiency virus (HIV) seropositivity, or active hepatitis B or C infection based on testing performed within 4 weeks of enrollment. 7. Currently enrolled in another investigational therapy protocol for AML. 8. Participants with presence of other active malignancy within 2 years of study entry; participants with history of prior malignancy treated with curative intent and achieved CR within 2 years are eligible. 9. Pregnant and lactating women are excluded from this study 10. Failure of research participant or legally responsible parent or guardian to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I study. 11. History of allergic reactions attributed to compounds of similar chemical or biological composition to cetuximab (anti-EGFR). 12. History of allergic reactions to products containing mouse and bovine protein antibodies. 13. Receiving corticosteroids at \>20 mg (age \>17) or \>0.5mg/kg (age \<18) daily prednisone dose or equivalent. 14. Active autoimmune disease requiring systemic immunosuppressive therapy. 15. Patient, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study.