Inclusion Criteria:

* Participants must be diagnosed with either relapsed or refractory AML (including extramedullary disease) or higher risk MDS.
* Absolute lymphocyte count ≥ 0.2 k/μL.
* Karnofsky performance status score ≥60%.
* Life expectancy ≥ 12 weeks from the time of enrollment.
* Pretreatment calculated or measured creatinine clearance (absolute value) of ≥ 40 mL/minute or Cr \> 2x upper limit of normal (ULN).
* Bilirubin ≤ 2.0 mg/dL or total bilirubin ≤ 3.0 x IULN with direct bilirubin within normal range in participants with well documented Gilbert's syndrome or hemolysis or who require regular blood transfusions
* Alanine aminotransferase (AST) and aspartate aminotransferase (ALT) \< 3.0 x IULN.
* Ejection fraction measured by echocardiogram (ECHO) or multi gated acquisition scan (MUGA) \> 45%.
* Participant does not require supplemental oxygen or mechanical ventilation AND has an oxygen saturation by pulse oximetry of ≥ 92% or higher on room air.
* Negative serum pregnancy test. Note: Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for at least 1 year following study treatment (T cell infusion); should a woman participant or female partner of a male participant become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately.
* Participant has a matched bone marrow donor and is otherwise able to receive a bone marrow transplant (dose escalation part only)
* Participants who have undergone allo-SCT are eligible if they are at least 3 months post SCT, have relapsed AML/MDS as defined above, are not on treatment or prophylaxis for GVHD for at least 6 weeks before administration of CAR T cells, and have no active GVHD.
* All participants must have the ability to understand and willingness to sign a written informed consent.

Exclusion Criteria:

* Diagnosis of acute promyelocytic leukemia (APL M3): t(15;17)(q22;q12); (promyelocytic leukemia \[PML\]/retinoic acid receptor \[RAR\] alpha \[a\]) and variants excluded.
* Known central nervous system (CNS) leukemic involvement that is refractory to intrathecal chemotherapy and/or cranio-spinal radiation; participants with a history of CNS disease that have been effectively treated to complete remission ( i.e. no blasts in cerebrospinal fluid \[CSF\] by cytology and flow cytometry) will be eligible.
* Prior treatment with investigational CAR T therapy for any disease.
* Participants enrolled in another investigational therapy protocol for their disease within 14 days or 5 half-lives of enrollment, whichever is shorter.
* Ongoing uncontrolled serious infection, symptomatic congestive heart failure, unstable angina pectoris, uncontrolled cardiac arrhythmia, poorly controlled pulmonary disease or psychiatric illness/social situations that would limit compliance with study requirements.
* Human immunodeficiency virus (HIV) seropositivity, or active hepatitis B or C infection based on testing performed within 28 days of enrollment.
* Participants requiring agents other than hydroxyurea to control blast counts within 14 days of study enrollment.
* Participants with presence of other active malignancy within 1 year of study entry;
* Participants with adequately resected basal or squamous cell carcinoma of the skin, or adequately resected carcinoma in situ (e.g. cervix) may enroll irrespective of the time of diagnosis.
* Pregnant and lactating women are excluded from this study
* History of allergic reactions attributed to compounds of similar chemical or biological composition to cetuximab (anti-EGFR).
* Active autoimmune disease requiring systemic immunosuppressive therapy (i.e. \>10mg of prednisone daily or equivalent).
* Participant, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study.