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

Exclusion Criteria

• •Patients who have had chemotherapy or other systemic therapy or radiotherapy, or those who have not recovered from adverse events due to prior administered agents as follows: chemotherapy, radiotherapy or surgery =\< 3 weeks prior to entering the study, targeted therapy (e.g., TKI) =\< 1 week prior to entering the study; autologous HSCT =\< 6 weeks prior to entering the study; investigational drug or immunotherapy (e.g. rituximab) =\< 4 weeks prior to entering the study; prophylactic intrathecal chemotherapy within one week of enrollment allowed; patients will be allowed to receive cytoreduction with hydroxyurea, 6-mercaptopurine, corticosteroids (dexamethasone, prednisone or similar) or cyclophosphamide provided that it is discontinued at least 24 hours prior to the initiation of study treatment; pre-phase treatment with dexamethasone 10 mg/m\^2 (maximum total 24 mg per day) for up to 5 days is required for patients with bone marrow blasts more than 50%, peripheral blood blasts of 15,000/uL or higher, or elevated lactate dehydrogenase suggesting rapidly progressing disease as per investigator's assessment; pre-phase treatment must be stopped at least 24 hours prior to the initiation of blinatumomab
• •Patients who are receiving any other investigational agents
• •Patients should be excluded if they have had prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune checkpoint pathways
• •Patients with active central nervous system leukemia are excluded from this clinical trial because they may develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; patients with a history of central nervous system (CNS) leukemia but no active disease at the time of enrollment are eligible; the absence of CNS disease must be confirmed by flow cytometric and cytologic examination of the cerebrospinal fluid (CSF) within 7 days of study enrollment
• •Active leukemia in the testes or isolated extramedullary relapse; patients with a history of treated leukemia in testes but no active disease at the time of enrollment are eligible
• •History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab, ipilimumab, or blinatumomab
• •History of severe hypersensitivity reaction to any monoclonal antibody
• •Uncontrolled intercurrent illness including, but not limited to, active, uncontrolled infection; symptomatic congestive heart failure; unstable angina pectoris; cardiac arrhythmia; or psychiatric illness/social situations that would limit compliance with study requirements; patients with infection under treatment and controlled with antibiotics are eligible
• •Pregnant women are excluded from this study because nivolumab and ipilimumab have the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab and ipilimumab, breastfeeding should be discontinued if the mother is treated with nivolumab and ipilimumab; these potential risks may also apply to blinatumomab
• •History of any chronic hepatitis including alcoholic, non-alcoholic steatohepatitis (NASH), drug related, autoimmune, chronic viral positive tests for hepatitis B virus surface antigen (HBsAg), hepatitis B core antibody (anti-HBc) in the absence of hepatitis B surface antibody (anti-HBs), or a positive hepatitis C (HCV) viral load; these patients are excluded due to the risk for autoimmune hepatitis with immune checkpoint inhibitors exacerbating their known liver disease as well as the unknown risk for hepatitis B and/or C reactivation with blinatumomab and immune checkpoint inhibitors
• •Subjects with active autoimmune disease, a history of known or suspected autoimmune disease or a history of a syndrome requiring systemic corticosteroids (\> 10 mg daily of prednisone equivalent) except for the treatment of malignancy with the exception of:
• •* Isolated vitiligo
• •* Resolved childhood atopy
• •* History of a positive antinuclear antibody (ANA) titer without associated symptoms or history of symptoms of an autoimmune disorder
• •* Controlled thyroid disorders
• •* Type I diabetes mellitus
• •* Psoriasis, Sjogren's syndrome, and arthropathies not requiring systemic treatment
• •* Autoimmune diseases: these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, autoimmune vasculitis, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease
• •Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; inhaled or topical steroids and adrenal replacement doses =\< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease; patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); physiologic replacement doses of systemic corticosteroids are permitted, even if \> 10 mg/day prednisone equivalents; a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen), or as pre-phase treatment for cytoreduction; patients will receive steroids with blinatumomab to reduce cytokine release syndrome (CRS) as specified in the protocol
• •Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI) obstruction and abdominal carcinomatosis which are known risk factors for bowel perforation should be evaluated for the potential need for additional treatment before coming on study
• •Patients who have a history of clinically relevant CNS pathology such as epilepsy, seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, psychosis, or other significant CNS abnormalities; a history of treated CNS leukemia will be allowed if recent CNS studies confirm the absence of active CNS disease at the time of study entry (screening)
• •Patients with a known concurrent malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or carcinoma in situ of the cervix
• •Subjects with interstitial lung disease that is symptomatic or may interfere with the detection or management of suspected drug-related pulmonary toxicity