Inclusion Criteria:

          -  Diagnosis of B-ALL in hematologic complete remission (defined as an M1 marrow, < 5%
             blasts) with MRD in the bone marrow (≥ 0.01%) by multi-parameter flow cytometry and
             that meets one of the following:

               -  Patients in first relapse or greater;

        OR

        • Patients with very-high risk biology ALL that is proceeding to HCT in first remission
        (e.g. Induction failure, Severe-hypodiploidy, Ph-like ALL);

        OR

        • Patients who have persistent MRD after Consolidation therapy (End of Consolidation (EOC)
        MRD positive ≥ 0.01%);

        AND with the intent of going on to an allogeneic hematopoietic cell transplantation (HCT)
        independent of this study

          -  Patients must have an available donor and have intention of proceeding directly to HCT
             after completion of 1 to 2 cycles of Bridging therapy with blinatumomab.

          -  Age ≤ 25 years at time of study enrollment

          -  Karnofsky Performance Status ≥ 50% for patients 16 years and older and Lansky Play
             Score ≥ 50 for patients under 16 years of age (see Appendix 1)

          -  Have acceptable organ function as defined within 7 days of study registration:

        Renal: creatinine clearance ≥ 60 mL/min/1.73m2 or serum creatinine based on age/gender

        Hepatic: ALT < 5 x upper limit of normal (ULN) and total bilirubin ≤ 1.5 x upper limit of
        normal (ULN) for age

        Cardiac: left ventricular ejection fraction ≥ 40% by ECHO/MUGA

          -  At least 7 days must have elapsed from prior chemotherapy.

          -  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.

          -  Biologic (anti-neoplastic agent): At least 7 days after the last dose of a biologic
             agent. For agents that have known adverse events occurring beyond 7 days after
             administration, this period must be extended beyond the time during which adverse
             events are known to occur. The duration of this interval must be discussed with the
             study chair.

          -  Monoclonal antibodies: At least 3 half-lives of the antibody must have elapsed after
             the last dose of monoclonal antibody (i.e. Inotuzumab = 12 days).

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

          -  XRT: Cranio or craniospinal XRT is prohibited during protocol therapy. ≥ 90 days must
             have elapsed if prior TBI, cranio 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 last dose of chemotherapy. Sexually active men
             must agree to use barrier contraceptive for the duration of treatment and for 2 months
             after the last dose of chemotherapy.

          -  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.

        Exclusion Criteria:

          -  History of CNS3 disease and/or active central nervous system (CNS) disease (≥ CNS2)

          -  Receiving concomitant chemotherapy, radiation therapy; immunotherapy or other
             anti-cancer therapy other than is specified in the protocol.

          -  Systemic fungal, bacterial, viral, or other infection not controlled (defined as
             exhibiting ongoing signs/symptoms related to the infection and without improvement,
             despite appropriate antibiotics or other treatment)

          -  Pregnant or lactating. The agents used in this study are known to be teratogenic to a
             fetus and there is no information on the excretion of agents into breast milk. All
             females of childbearing potential must have a blood test or urine study within 7-days
             prior to the start of blinatumomab to rule out pregnancy.

          -  Known allergy to blinatumomab

          -  Participating in a concomitant Phase 1 or 2 study