Blinatumomab and Nivolumab With or Without Ipilimumab in Treating Patients With Poor-Risk Relapsed or Refractory CD19+ Precursor B-Lymphoblastic Leukemia

Inclusion Criteria: * PRE-REGISTRATION ELIGIBILITY CRITERIA * Patients must have suspected refractory or relapsed pre-B cell ALL or mixed phenotype acute leukemia (MPAL), or if newly diagnosed, the patient must be 60 years of age or older * Bone marrow and/or peripheral blood specimens will be submitted for correlative studies; patients who have a dry tap will still be eligible * REGISTRATION ELIGIBILITY CRITERIA * Patients must have histologically or cytologically confirmed by the local institution CD19+ precursor B-acute lymphoblastic leukemia (pre-B cell ALL) OR CD19+ mixed phenotype acute leukemia (MPAL): a) with relapse following or refractory to at least one prior line of therapy if older than 21 years; b) in second or higher relapse or refractory to at least two prior lines of therapy if 21 years old and younger (16-21); c) or they must have a new diagnosis of pre-B cell ALL or CD19+ MPAL but are \>= 60 years old and are either not a candidate for or do not wish to receive traditional induction chemotherapy * The evidence of CD19+ expression on leukemia cells must be confirmed by pathology review of the bone marrow and/or peripheral blood specimens (flow cytometry and/or immunohistochemistry) collected at the time of current relapse and prior to the initiation of therapy * Patients with Philadelphia chromosome (Ph) positive (+) pre-B cell ALL OR Ph+ MPAL will be eligible if they have been refractory to or intolerant of treatment with at least 1 second-generation or th…