This Research study is being done to characterize the safety, tolerability, and preliminary antitumor activity of the NEXI-001 T cell product (a new experimental therapy), which contains populations of CD8+ T cells targeting multiple leukemia associated antigen peptides in patients with Acute Myeloid Leukemia (AML) or Myelodysplastic Syndrome (MDS) who have relapsed disease after an allogeneic hematopoietic cell transplant (HCT).

The study will enroll AML or MDS patients who have either Minimal Residual Disease (MRD) or relapsed disease after a human leukocyte antigen (HLA)-matched allogeneic HCT. Patients who have had an HLA-mismatched or haploidentical allogeneic HCT will not be eligible to participate in this study. Eligible patients for this study must also have ≥ 50% T-cell chimerism from the original donor at the time study entry.

The enrolled patients will undergo bridging therapy for the purposes of disease control while the NEXI-001 T cell product is being manufactured. Choice of bridging therapy administered will be per the Investigator's discretion, but is limited to acceptable agents as specified in the protocol. Bridging therapy will be administered prior to lymphodepleting (LD) therapy, with the last dose of the bridging therapy administered ≥ 14 days prior to initiation of LD therapy. Within 72 hours after completing LD therapy, patients will receive a single IV infusion of the NEXI-001 T cell product.

The NEXI-001 is an adoptive cellular therapy product which contains populations of antigen-specific CD8+ T cells. The antigen-specific CD8+ T cells in the NEXI-001 T cell product are derived from Peripheral Blood Mononuclear Cells (PBMC) obtained from the original stem cell donor. During the manufacturing process, these cells are primed and expanded ex vivo using nano-size artificial Antigen Presenting Cells (aAPC) loaded with five leukemia associated antigen peptides in combination with a proprietary T cell enrichment and expansion process.

The NEXI-001 T cell product is restricted to patients that are HLA-A2.01 allele positive for this study.

There are two parts to this study, a Safety Evaluation Phase and a Dose Expansion Phase. The Safety Evaluation Phase will determine the safety and tolerability of a single dose of NEXI-001 T cell product, and will consist of Dose Escalation at two dose levels - each with cohorts of three patients.

When all three patients at Dose Level 1 have dosed and cleared the DLT period, three additional patients will be enrolled at Dose Level 2. When three patients have cleared the DLT period at the highest dose level, that dose will be advanced to the Dose Expansion Phase. The Dose Expansion Phase will enroll up to 16 additional patients to further define the safety and evaluate the initial anti-tumor efficacy of the NEXI- 001 T cell product at the dose established from the Safety Evaluation Phase.

All patients will enter a Post-Treatment Follow-Up period after infusion of the NEXI- 001 T cell product. During this phase, all patients will be monitored for AEs and followed for anti-leukemia response until the end of study visit is complete (up to one year).

Additional assessments for safety, disease status, and other secondary and exploratory endpoints will also be monitored during the follow-up period.

All patients will be followed for overall survival (OS) from time of disease progression until the last visit of the last patient. During this time, patients will be followed via telephone or other electronic contact at 12 week intervals for monitoring of OS.

Inclusion Criteria:

General

1. Ability to provide informed consent and documentation of informed consent prior to initiation of any study-related tests or procedures that are not part of standard-of-care for the patient's disease. Patients must also be willing and able to comply with study procedures, including the acquisition of specified research specimens

2. Age ≥ 18 years old

3. Expression of HLA-A*0201 as determined by high resolution sequence-based typing method (e.g. TruSight HLA v2 Sequence Panel)

4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

5. Patients must have a confirmed diagnosis of AML (according to World Health Organization (WHO) classification) or MDS with evidence of MRD or morphological relapse after HLA-matched allogeneic HCT

   MRD includes:

   1. Detection of blasts <5% in bone marrow
   2. Detection of a clonal abnormal blast population via multi-color flow cytometry
   3. Detection of known or new myeloid gene mutations

6. Donor match at 10 of 10 loci for HLA-A, -B, -C, -DRB1 and DQB1, with each typed at high resolution by DNA-based methods.

   a. Patients who have had prior HLA-mismatched or haploidentical allogeneic HCT will not be eligible

7. T-cell chimerism ≥ 50% to donor (by PCR analysis)

8. Acceptable laboratory parameters as follows:

   1. Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) ≤ 2.5 × upper limit of normal (ULN)
   2. Total bilirubin ≤ 1.5 × ULN, except patients with Gilbert's syndrome, who may enroll if the conjugated bilirubin is within normal limits
   3. Creatinine < 1.5 mg/dL or a calculated or measured creatinine clearance (CL) ≥ 50 mL/min per standard calculation

9. Recovery to Grade 1 or baseline of non-hematologic toxicities from prior treatments, excluding alopecia

10. Female patients of childbearing potential must test negative for pregnancy at enrollment and during the study. Sexually active women of child-bearing potential, unless surgically sterile, must be willing to use a highly effective method of birth control defined as those which result in a low failure rate (i.e., less than 1% per year) such as implants, injectables, combined oral contraceptives, intra-uterine devices (IUDs) or vasectomized partner

11. Male patients with partners of childbearing potential must be either vasectomized or agree to use a condom in addition to having their partners use another method of contraception resulting in a highly effective method of birth control defined as those which result in a low failure rate (i.e., less than 1% per year) such as implants, injectables, combined oral contraceptives, or IUDs. Patients should not have sexual intercourse with females who are either pregnant or lactating without double-barrier contraception Is not pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the prescreening or screening visit through one year from administration of NEXI-001 cells

Exclusion Criteria:

1. Active acute or chronic graft versus host disease (GvHD)

   1. Eligible patients will not be on any steroids ≥10 mg per day prednisone or equivalent or other immunosuppressants such as tacrolimus, cyclosporine, etc.
   2. Intermittent topical, inhaled or intranasal corticosteroids are allowed

2. Have active or uncontrolled infections with positive cultures and/or requiring treatment with IV anti-infective agents

3. History of clinically significant cardiovascular disease including but not limited to:

   1. Myocardial infarction or unstable angina within the 6 months prior to the initiation of study
   2. Stroke or transient ischemic attack within 6 months prior to initiation of study
   3. Clinically significant cardiac arrhythmia
   4. Uncontrolled hypertension: systolic blood pressure (SBP) > 180 mmHg, diastolic blood pressure (DBP) > 100 mmHg
   5. Congestive heart failure (New York Heart Association [NYHA] class III-IV)
   6. Pericarditis or clinically significant pericardial effusion
   7. Myocarditis

4. Clinically significant pulmonary compromise, including a requirement for supplemental oxygen use to maintain adequate oxygenation

5. History of autoimmune disease (e.g. Crohn's, rheumatoid arthritis, systemic lupus erythematosus, etc.) resulting in end organ injury or requiring systemic immunosuppression / systemic disease modifying agents within the last 2 years prior to enrollment. Subjects with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone and subjects with controlled Type 1 diabetes mellitus on a stable insulin regimen may be eligible for the study

6. Human immunodeficiency virus (HIV) seropositive; HIV testing within 2 years of enrollment

7. Seropositive for and with evidence of active viral infection with hepatitis B virus (HBV). Patients who are hepatitis B surface antigen (HBsAg) negative and HBV viral DNA negative are eligible

   1. Patients who had HBV but have received an antiviral treatment and show non-detectable viral DNA for 6 months are eligible
   2. Patients who are seropositive because of HBV vaccine are eligible

8. Seropositive for and with active viral infection with hepatitis C virus (HCV)

   a. Patients who had HCV but have received an antiviral treatment and show no detectable HCV viral DNA for 6 months are eligible

9. Second primary invasive malignancy that has not been in remission for greater than 2 years. Exceptions that do not require a 2-year remission include: resected non-melanoma skin cancer; carcinoma in situ (cervix, bladder, breast, etc.) or squamous intraepithelial lesion on Pap smear; localized prostate cancer (Gleason score < 6); or resected melanoma in situ

10. History of trauma or major surgery within 4 weeks prior to the study enrollment

11. Any serious underlying medical or psychiatric condition that would impair the ability of the patient to receive or tolerate the planned treatment and follow up

12. Known hypersensitivity to any component of NEXI-001 T cells, cyclophosphamide, fludarabine or tocilizumab

13. Vaccination with any live virus vaccine is not permitted prior to the initiation of study treatment. Inactivated annual influenza vaccination is allowed.

14. Dementia or altered mental status that would preclude understanding and rendering of informed consent

15. History of seizures, aphasia, psychosis or other chronic clinically significant neurologic disorders

    a. Patients with remote history of seizures that are well controlled on anti-seizure medications and without any seizure episode for 6 months are eligible

16. Any issue that in the opinion of the investigator, would contraindicate the patient's participation in the study or confound the results of the study