• Number of Participants who Experience Dose Limiting Toxicities (DLTs) [ Time Frame: Up to Day 42 ]
  A dose limiting toxicity (DLT) is any of the following and is determined by the investigator to be related to study drug:

  • Aplastic bone marrow, defined by marrow cellularity <5% at Day 28 in the absence of residual disease and confirmed at Day 42.
  • Treatment-emergent CRS of Grade 4 that does not resolve to Grade ≤2 within 72 hours, despite optimal treatment;
  • Treatment-emergent CRS of Grade 3 that does not resolve to Grade ≤2 within 2 weeks, despite optimal treatment;
  • Treatment-related Grade 4-5 allergic reactions
  • Treatment-related non-reversible Grade 3 (< 14 days), or any Grade 4-5 autoimmune reactions related to the study cell infusion.
  • Central neurologic toxicity Grade ≥3 lasting more than 14 days
  • Grade 5 Cytokine Release Syndrome (CRS)
  • Tumor Lysis Syndrome ≥ IV (Cairo and Bishop, 2004[2]) that does not resolve within 7 days
• Number of Participants who Experience Treatment Related Adverse Events (AEs) [ Time Frame: Up to 12 months post treatment ]
  Systemic toxicity in general and hematologic toxicity in specific will be assessed through the capture of AEs at each study visit and through laboratory assessments throughout the study. The severity of the AEs will be assessed using the Common Terminology Criteria for Adverse Events (CTCAE) v 5.0 scale.

• Disease Progression in AML Participants [ Time Frame: Up to 15 years ]
  Proportion of AML patients achieving partial response (PR), complete response (CR), and/or morphologic leukemia free state (MLFS) by ELN Response Criteria in AML. CRh (complete PRGN-3006 T cells in patients with AML/MDS remission with partial hematological recovery) will also be captured, defined as <5% of blasts in the bone marrow, no evidence of disease, and partial recovery of peripheral blood counts
• Disease Response in MDS Patients [ Time Frame: Up to 15 years ]
  Proportion of MDS patients achieving a response (CR, PR or Marrow CR) as defined in International Working Group (IWG) 2006 Criteria.
• Rate of Absolute Neutrophil Count Recovery [ Time Frame: Day 28 ]
  Rate of Absolute Neutrophil count recovery (>0.5 x 10^9/L)
• Absolute Lymphocyte Count (ALC) [ Time Frame: Baseline ]
  ALC including CD4/CD8 subsets by flow cytometry at baseline (at apheresis) in patients who have successful versus failed PRGN-3006 production.
• Number of PRGN-3006 T Cells [ Time Frame: Up to 12 months post treatment ]
  Number of PRGN-3006 T Cells present in patients treated with PRGN-3006

This is a single center, nonrandomized, investigator-initiated Phase 1/1b safety and tolerability study. The safety and tolerability of PRGN-3006 T cells will be assessed following intravenous administration of escalating doses in patients with relapsed or refractory acute myeloid leukemia (AML) or higher risk myelodysplastic syndromes (MDS).

This study will enroll in two phases: an initial dose escalation phase followed by a dose expansion phase.

• Myelodysplastic Syndromes
• Acute Myeloid Leukemia

Inclusion Criteria:

• Participants must be diagnosed with either relapsed or refractory AML 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).
• Serum 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.