Antigen-specific T Cell Therapy for AML or MDS Patients With Relapsed Disease After Allo-HCT

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.