Blinatumomab Plus HLA-Mismatched Cellular Therapy for Relapsed/Refractory CD19+ ALL

Inclusion Criteria: * Relapsed/Refractory CD19+ Acute Lymphoblastic Leukemia. Patients with minimal residual disease detected by NGS \> 10e-6 or multiparameter flow cytometry \> 10e-5 in blood or bone marrow are eligible. * Patients must belong to one of the following 'high risk' categories: (i) at least 2nd relapse or refractory to at least one salvage therapy (ii) relapse after autologous stem cell transplantation, (iii) any relapse in a patient with no immediate allogeneic transplant option (such as advanced age, comorbidity, lack of identified donor, or patient refusal) (iv) Patients with Ph+ ALL will be allowed on the trial at the discretion of the treating physician if they are no longer candidates for further TKI based therapy. Prior therapy with a minimum of 2 prior 2nd/3rd generation TKI is required. (TKI therapy is not allowed while on trial). * Patients with prior blinatumomab treatment are eligible if last treatment was at least 3 months prior to C1D1, patient's blasts are confirmed to express CD19, and patient did not develop Grade 4 toxicities with prior blinatumomab therapy. * Age ≥ 18 years. * Patient has at least one medically fit first- or second-degree family member who is a potential haploidentical donor. In addition, the prospective donor is willing to voluntarily donate peripheral blood cells, and sign consent forms. For minors, consent will be obtained from parent/guardian (assent from the minor is required). * Patients must have adequate organ function as defined below (note there are no marrow function criteria, cytopenias will not result in exclusion): * Serum creatinine ≤ 2.0 x the upper limits of institutional normal (ULN) * Total bilirubin ≤ 1.5x the upper limits of institutional normal, unless elevated bilirubin is attributed to liver involvement of leukemia or Gilbert's disease. * AST/ALT ≤ 2.5 x the upper limits of institutional normal (≤ 5 x ULN for patients with suspected liver involvement of leukemia). * ECOG performance status of 0, 1, or 2, and estimated survival of at least 3 months. * Patients must be able to understand and agree to sign an IRB-approved informed consent form. * The effects of treatment on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or complete abstinence) prior to study entry, for the duration of study, and for two months after study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Written informed consent obtained from subject and ability for subject to comply with the requirements of the study. Exclusion Criteria: * Prior allogeneic stem cell transplant * Prior treatment with fludarabine or cladribine within the last six months prior to C1D1, or treatment with antithymocyte globulin (ATG) or alemtuzumab within the last 1 year. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant and/or lactating. * Who have had non-biopsy surgery in the last 10 days. * Who have active CNS disease. Patients with previously treated leptomeningeal disease without evidence of remaining leukemia cells by spinal fluid will be eligible. Intrathecal chemo may be given for prophylaxis for patients who previously had CNS involvement but have now cleared the CSF, at the discretion of the treating physician. Recommend to avoid IT chemotherapy for a few days before or after HMCT infusion. * History or presence of clinically relevant CNS pathology such as epilepsy, childhood or adult seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, organic brain syndrome, or psychosis (patients with minor prior stroke who are cognitively intact and capable of performing all ADLs are permitted). * Patients with known active autoimmune disorder. * Known infection with HIV virus. * Patients concurrently taking the following drugs are excluded: mycophenolate, cyclosporine, prednisone \> 20mg/day, or immunosuppressive agents (low dose maintenance chemotherapy - POMP, hydroxyurea, low dose prednisone - is allowed until 24 hours prior to starting blinatumomab). * Patients known to have active hepatitis B or C (Hepatitis B positive patients are allowed if they are on appropriate antiviral agents such as lamivudine). * Subject likely to not be available to complete all protocol-required study visits or procedures, including follow-up visits, and/or to comply with all required study procedures to the best of the subject and Investigator's knowledge. History or evidence of any other clinically significant disorder, condition or disease (with the exception of those outlined above) that, in the opinion of the Investigator or Amgen physician, if consulted, would pose a risk to subject safety or interfere with the study evaluation, procedures or completion.