Blinatumomab After TCR Alpha Beta/CD19 Depleted HCT

Inclusion Criteria: * 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: 1. In remission after first relapse or greater (≥ CR2) 2. Very-high risk biology ALL that is proceeding to HCT in first remission (e.g. Induction failure, Severe-hypodiploidy, Ph-like ALL) 3. 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 Exclusion Criteria: * Active extramedullary disease or presence of chloromatous disease. * Receiving concomitant chemotherapy, radiation therapy; immunotherapy or other anti-cancer therapy for treatment of disease 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). Patients with possible fungal infections must have had at least 2 weeks of appropriate anti-fungal antibiotics and be asymptomatic. * 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 registration to rule out pregnancy. * Known allergy to any chemotherapies or targeted agents included in this protocol. * Participating in a concomitant Phase 1 or 2 study involving treatment of disease. * Active malignancy other than B-ALL.