The goal of this clinical trial is to test BSB-1001 which is a new type of cellular therapy to treat blood cancers (AML, ALL and MDS). It will evaluate the safety of BSB-1001 and also determine whether it works to prevent relapse of your cancer.

This is a first-in-human, multicenter, open-label, dose-finding study for the evaluation of an HA-1 minor histocompatibility antigen (miHA)-reactive TCR-modified T cell product (BSB-1001) derived from an HLA-matched allogenic donor, in patients with AML, ALL or MDS undergoing an HLA-matched alloHSCT who are at a high risk for relapse post-HSCT. BSB-1001 targets the HLA-A*02:01-restricted HA-1 miHA.

Enrolled patients must be HLA-A*02:01 and HA-1-positive (H/H or H/R), with an identified HLA-matched, HA-1-negative (R/R) donor. Patients will undergo one of the following myeloablative conditioning regimens, according to standard institutional procedures, which include either fludarabine+thiotepa+total body irradiation, or busulfan+ melphalan+ fludarabine. After conditioning is completed, patients will receive the CD34-selected alloHSCT followed by BSB-1001 on day 0, without any prophylactic immunosuppression.

The study is an adaptive dose escalation design with 1 to 3 cohorts to evaluate single doses of BSB-1001. Three to six patients will be enrolled in each cohort and enrolled patients will be followed until completion of the study.

If the maximum tolerated dose (MTD) is reached or if a dose is deemed promising, the Sponsor may determine to either cease enrollment or open an expansion cohort at the desired dose level. The optional expansion part of the study is planned to include approximately 20 additional AML patients at the recommended dose.

Inclusion Criteria:

1. Male or female patients, ages 18 - 70 years inclusive, undergoing alloHCT.

2. Any of the following high-risk hematologic malignancies:

   1. AML diagnosed which has been treated with at least two lines of therapy* Refractory or relapsed (CR, CRh or CRi,), including myeloblasts up to 25% OR MRD positive OR persistent disease-defining cytogenetic abnormality OR MRD-negative, but with high-risk disease For patients in remission meeting criteria a, consolidation regimens would be considered another line of therapy of eligibility purposes
   2. ALL which has been with abnormal lymphoblasts ≥5% and up to 25% in bone marrow OR persistent disease-defining cytogenetic abnormality or MRD positive
   3. MDS after at least one line of therapy, which includes hypomethylating agent(s) and must be high or very high risk by Revised International Prognostic Scoring System (IPSS-R), monosomy, or complex karyotype or TP53 mutation.
   4. In the expansion phase AML patients diagnosed which has been treated with at least two lines of therapy, and refractory or relapsed (CR, CRh or CRi,), including myeloblasts up to 25% OR MRD positive OR persistent disease-defining cytogenetic abnormality OR MRD-negative, but with high- risk disease

3. HLA-A*02:01 AND HA-1 positive (either H/H or H/R).

4. Suitable for one of the approved conditioning regimens as defined in the protocol.

5. Patient must have an identified donor that is HA 1-negative with 10/10 matched related or unrelated donor

Exclusion Criteria:

1. Weight > 100 kg.
2. Prior history of allogeneic stem cell transplantation
3. Prior history of autologous stem cell transplantation within 1 year prior to the planned dosing of BSB-1001 (day 0)
4. Previous genetically engineered chimeric antigen receptor T Cell therapy (CAR-T), approved or investigational, within 2 years of screening, with the exception of patients with ALL previously treated with an autologous CAR-T product.
5. Treatment with other investigational agents within 5 half-lives of the planned dosing of BSB-1001 (day 0).
6. History of treatment with checkpoint inhibitor therapy within 3 months of transplantation.
7. Other malignancy with life expectancy < 1year.
8. Pregnant or lactating women.
9. Uncontrolled bacterial, viral, or fungal infections at time of enrollment.
10. Past or current viral infections as defined in the protocol.
11. CNS involvement refractory to intrathecal chemotherapy and/or standard cranial- spinal radiation. 12 Karnofsky Performance Score < 60%.

13. Inadequate organ function as defined in protocol.