• 18 years of age or older at enrollment. Patients ≥12 and \<18 12 to 17 years of age weighing ≥ 35 kg at enrollment may be included once safety evaluation at the corresponding adult dose escalation protocol have been completed.

• Subjects with AML unlikely to be cured with currently available therapies. Specifically, the following groups are eligible:

‣ Refractory AML: i.e., newly diagnosed AML that after two cycles of intensive chemotherapy has not achieved a complete remission or morphologic leukemia free state by ELN criteria.1 Intensive chemotherapy must have included either the combination of cytarabine and an anthracycline (7+3 or similar) or combination of venetoclax with a hypomethylating agent.

‣ Patients with FLT3 ITD must also have failed treatment with a FLT3 inhibitor and patients with IDH1 or IDH2 mutations must have failed treatment containing ivosidenib or enasidenib respectively (i.e., progression on treatment, or failure to achieve CR after six months of treatment,) OR:

⁃ AML relapsed following allogeneic stem cell transplantation (including MDS evolved to AML post-allogeneic stem cell transplantation). Note: morphologic relapse is not required; persistent/recurrent disease-associated molecular, phenotypic, or cytogenetic abnormalities (measurable residual disease, MRD) at any time after allogeneic HSCT is eligible. OR:

⁃ AML that has relapsed within 12 months after initial induction and consolidation therapy OR:

⁃ AML that has relapsed more than 12 months after initial induction but that has failed to achieve CR or morphologic leukemia free state after one reinduction OR:

⁃ AML after second or subsequent relapse.

• FLT3 expression must be detectable in AML blast by flow cytometric analysis.

• Subjects must have a suitable stem cell transplant donor. Donor may be matched or mismatched and must be found to be suitable according to the institution's standard criteria. That donor shall be cleared for donation by institutional standards prior to administration of HG-CT-1. Adult donors can be either related or unrelated, HLA-matched or partially matched. Matched or partially matched umbilical cord blood donors are also eligible.

• Subjects with relapsed disease after prior allogeneic transplant must be off systemic immunosuppression for at least 1 month at the time of enrollment without GvHD that requires systemic immunosuppression.

• Satisfactory organ functions:

‣ Creatinine ≤ 1.6 mg/dl and Creatinine clearance (CrCl) as calculated by the Cockcroft-Gault formula ≥ 60 mL/min.

⁃ ALT/AST must be ≤ 3 x upper limit of normal unless related to disease.

⁃ Direct bilirubin \< 2.0mg/dl unless subject has Gilbert's syndrome (in which case it should be ≤3.0 mg/dL).

⁃ Left ventricular ejection fraction ≥ 45% as confirmed by echocardiogram or MUGA.

⁃ DLCO \>45% predicted and O2 Saturation \> 90% on room air.

• Patients ≥18 must have an ECOG Performance status 0-1. Patients \<18 must have a Lansky/Karnofsky score of ≥50.

• Written informed consent is given in patients ≥ 18. In patients \<18 or not developmentally appropriate for consent, written consent will be provided to the parent or legal guardian. Patients ≥12 and \<18 years of age will be additionally provided with assent documentation.

• Subjects of reproductive potential must agree to use acceptable birth control methods (as described in protocol Section 4.7).