HMCT/CT2401: Abatacept GVHD Prophylaxis Following Omidubicel HCT

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.