• Diagnosis of B-ALL with no evidence of minimal residual disease in the bone marrow by multi-parameter flow cytometry (FC-MRD negative, \<0.01%) and meet at least one of the following:

‣ In remission after first relapse or greater (≥ CR2)

⁃ Very-high risk biology ALL that is proceeding to HCT in first remission (e.g. Induction failure, Severe-hypodiploidy, Ph-like ALL)

⁃ First remission with persistent disease identified as end of consolidation (EOC) MRD \> 0.01%.

• Patients must have an available unrelated or haploidentical donor

• Age ≤ 25 years at time of study enrollment

• Karnofsky Performance Status ≥ 60% for patients 16 years and older and Lansky Play Score ≥ 60 for patients under 16 years of age

• Have acceptable organ function as defined within 14 days of study registration: Renal: creatinine clearance or radioisotope GFR ≥ 60 mL/min/1.73m2 Hepatic: ALT \< 5 x upper limit of normal (ULN) and total bilirubin ≤ 3 mg/dL Cardiac: left ventricular ejection fraction ≥ 40% by ECHO/MUGA Pulmonary: No evidence of dyspnea at rest. No supplemental oxygen requirement. If measured, carbon monoxide diffusion capacity (DLCO) \> 50%. Central Nervous System: Based on clinical exam, no concern for/evidence of active CNS infection. Patients with fully treated prior CNS infections are eligible. Patients with seizure disorders may be enrolled if seizures are well-controlled on anticonvulsant therapy.

• Patients who have experienced their relapse after HCT are eligible, provided they have no evidence of acute or chronic Graft-versus-Host Disease (GVHD) and are off all transplant immune suppression therapy for at least 7-days (e.g. steroids, cyclosporine, tacrolimus). Steroid therapy for non-GVHD and/or non-leukemia therapy is acceptable.

• Immunotherapy: At least 42 days after the completion of any type of immunotherapy aside from blinatumomab (e.g. tumor vaccines or CAR T-cell therapy).

• XRT: Cranial or craniospinal XRT is prohibited during protocol therapy. ≥ 90 days must have elapsed if prior TBI, cranial or craniospinal XRT

• Sexually active females of child bearing potential must agree to use adequate contraception (diaphragm, birth control pills, injections, intrauterine device \[IUD\], surgical sterilization, subcutaneous implants, or abstinence, etc.) for the duration of treatment and for 2 months after the completion of blinatumomab therapy. Sexually active men must agree to use barrier contraceptive for the duration of treatment and for 2 months after the completion of blinatumomab therapy.

• Voluntary written consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care.

• All patients enrolled in this study must have been enrolled in the Blinatumomab Bridging Therapy (BBT) Trial