This study is a single-center, non-randomized, single-arm pilot trial of omidubicel hematopoietic stem cell transplantation (HCT) for hematologic malignancies with myeloablative conditioning chemotherapy of physician's choice followed by abatacept/tacrolimus/mycophenolate mofetil (ABA/Tac/MMF) graft-versus-host disease (GVHD) prophylaxis. The primary objective is to assess the safety and feasibility of abatacept/tacrolimus/mycophenolate mofetil GVHD prophylaxis following omidubicel HCT.

Target enrollment is 10 participants. Subjects are adults with a diagnosis of hematologic malignancy with an available cord blood unit for omidubicel product manufacturing. Patients will be followed for a total of 18 months and will have research blood draws and Abatacept pharmacokinetics, as well as standard of care assessments that will be reviewed for this study.

It is estimated that 36 months of accrual will be necessary to enroll the targeted sample size with an accrual rate of approximately 1 participant every 3 months. Accrual will be reported by race, ethnicity, gender, and age. Descriptive analyses are planned given the sample size.

Inclusion Criteria:

1. A diagnosis of hematologic malignancy with an available cord blood unit for omidubicel product manufacturing

2. Adult patients (≥18 at the time of enrollment)

3. Adequate organ function for transplant defined as:

   1. Left ventricular ejection fraction ≥ 40%;
   2. DLCO, FEV1, FVC > 50% predicted;
   3. Total bilirubin ≤ 2.5 mg/dL except for patients with Gilbert's syndrome or hemolysis, and ALT, AST, and alkaline phosphatase all < 5 x upper limit of normal (ULN);
   4. Serum creatinine within normal range, or if serum creatinine outside normal range, must have measured or estimated creatinine clearance > 40 mL/min/1.73m2;
   5. Karnofsky performance score ≥ 70; and
   6. If applicable, > 6 months since a previous autologous transplant.

4. Female patients (unless postmenopausal or surgically sterilized) and male patients (even if surgically sterilized) must agree to practice two effective methods of contraception at the same time, or agree to completely abstain from heterosexual intercourse from the time of signing informed consent through 100 days post-transplant. Fertility preservation method will be left to treating physician's discretion.

Exclusion Criteria:

1. Patients with known sensitivity to dimethyl sulfoxide, dextran 40, gentamicin, human serum albumin or bovine material
2. Presence of a donor-specific antibodies with MFI >2000
3. Uncontrolled bacterial, fungal or viral infection
4. Treatment with any other investigational medical product (medications without any known FDA approved indication) needs to be discussed with the PI for patient eligibility.