Inclusion Criteria:

   - Patients must be >= 1 and < 31 years at time of enrollment

   - Patients must have first relapse of CD19+ B-ALL (relapse blasts must express CD19) in
   one of the following categories:

      - Isolated bone marrow relapse

      - Isolated central nervous system (CNS) (excluding known optic nerve/retinal and
      CNS chloromas) and/or testicular relapse

      - Combined bone marrow with extramedullary relapse in the CNS (excluding known
      optic nerve/retinal and CNS chloromas) and/or testes

   - Patients with Down syndrome (DS) are eligible in the following categories:

      - Isolated bone marrow relapse

      - Combined bone marrow with CNS (excluding known optic nerve/retinal and CNS
      chloromas) and/or testicular relapse

   - Patients must have a performance status corresponding to Eastern Cooperative Oncology
   Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients > 16 years of age and
   Lansky for patients =< 16 years of age

      - Of note, for patients with developmental delay (e.g., Down syndrome) regardless
      of age, Lansky scale may be substituted for Karnofsky scale. However, the
      requirement for ECOG 0-2 remains, regardless of known history of developmental
      delay

   - Patients must have fully recovered from the acute toxic effects of all prior
   chemotherapy, immunotherapy, or radiotherapy prior to entering this study

      - Patients with prior blinatumomab or CD19+ chimeric antigen receptor therapy in
      the upfront setting will be eligible, provided relapsed lymphoblasts retain CD19
      expression

      - Radiation therapy (RT): >= 3 months must have elapsed if prior RT. This includes
      any patient requiring urgent radiation to any sites of extramedullary disease
      prior to enrollment (e.g. retinal/optic nerve involvement)

      - Hematopoietic stem cell transplant (HSCT): Patients must not have had a prior
      hematopoietic stem cell transplant

      - A single intrathecal chemotherapy at the time of relapse will be allowed. If < 7
      days have elapsed between this intrathecal therapy (IT) and the start of protocol
      therapy, then the day 1 intrathecal chemotherapy (i.e. methotrexate, cytarabine,
      or triple intrathecal) may be omitted

      - In the 28 days prior to enrollment, up to five days of post-relapse,
      pre-enrollment therapy (steroid and/or hydroxyurea only) is permissible

         - Group 1 and Down syndrome patients who received pre-enrollment therapy and
         have a white blood count (WBC) >= 30,000/ul at the time of enrollment must
         receive protocol specified cytoreductive therapy with vincristine and
         dexamethasone, and no "washout" is required

         - Group 1 and Down syndrome patients who received pre-enrollment therapy and
         have a WBC < 30,000/ul at the time of enrollment must be given a 24 hour
         "washout" before starting immunotherapy

      - Note: There is no waiting period or "washout" for patients who relapse while
      receiving upfront therapy

   - Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70
   mL/min/1.73 m^2 OR a serum creatinine based on age/gender as follows (within 7
   calendar days prior to enrollment):

      - Age: Maximum serum creatinine (mg/dL)

         - 1 to < 2 years: 0.6 (male), 0.6 (female)

         - 2 to < 6 years: 0.8 (male), 0.8 (female)

         - 6 to < 10 years: 1 (male), 1 (female)

         - 10 to < 13 years: 1.2 (male), 1.2 (female)

         - 13 to < 16 years: 1.5 (male), 1.4 (female)

         - >= 16 years: 1.7 (male), 1.4 (female)

   - Shortening fraction of >= 27% by echocardiogram, or ejection fraction of >= 50% by
   echocardiogram, cardiac magnetic resonance imaging (MRI) or radionuclide angiogram

   - No evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry > 94% if
   there is clinical indication for determination

   - All patients and/or their parents or legal guardians must sign a written informed
   consent

   - All institutional, Food and Drug Administration (FDA), and National Cancer Institute
   (NCI) requirements for human studies must be met

Exclusion Criteria:

   - Patients with B-lymphoblastic lymphoma (B-LLy)

   - Patients with Burkitt leukemia/lymphoma or mature B-cell leukemia

   - Patients with Philadelphia chromosome positive (Ph+) B-ALL

   - Patients with mixed phenotype acute leukemia (MPAL)

   - Patients with known Charcot-Marie-Tooth disease

   - Patients with known MYC translocation associated with mature (Burkitt) B-cell ALL,
   regardless of blast immunophenotype

   - Patients with active, uncontrolled infection defined as:

      - Positive bacterial blood culture within 48 hours of study enrollment

      - Receiving IV or PO antibiotics for an infection with continued signs or symptoms.
      Note: Patients may be receiving IV or oral antibiotics to complete a course of
      therapy for a prior documented infection if cultures have been negative for at
      least 48 hours and signs or symptoms of active infection have resolved. For
      patients with clostridium (C.) difficile diarrhea, at least 72 hours of
      antibacterial therapy must have elapsed and stools must have normalized to
      baseline.

      - Fever above 38.2 degrees Celsius (C) within 48 hours of study enrollment with
      clinical signs of infection. Fever without clinical signs of infection that is
      attributed to tumor burden is allowed if blood cultures are negative for > 48
      hours

      - A positive fungal culture within 30 days of study enrollment or active therapy
      for presumed invasive fungal infection

      - Active viral or protozoal infection requiring IV treatment

   - Patients known to have one of the following concomitant genetic syndromes: Bloom
   syndrome, ataxia-telangiectasia, Fanconi anemia, Kostmann syndrome, Shwachman syndrome
   or any other known bone marrow failure syndrome are not eligible. Of note, patients
   with known human immunodeficiency virus (HIV) infection on effective anti-retroviral
   therapy with undetectable viral load for at least the last 6 months prior to
   enrollment are eligible. Similarly, hepatitis B and hepatitis C positive patients who
   have been treated and have no viral detectable burden are also eligible

   - Patients with significant central nervous system pathology that would preclude
   treatment with blinatumomab, including history of severe neurologic disorder or
   autoimmune disease with CNS involvement

      - Note: Patients with a history of seizures that are well controlled on stable
      doses of anti-epileptic drugs are eligible Patients with a history of
      cerebrovascular ischemia/hemorrhage with residual deficits are not eligible.
      Patients with a history of cerebrovascular ischemia/hemorrhage remain eligible
      provided all neurologic deficits have resolved

   - Patients with an active known/suspected autoimmune disease are not eligible. However,
   patients with type I diabetes mellitus, hypothyroidism only requiring hormone
   replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring
   systemic treatment, or conditions not expected to recur in the absence of an external
   trigger are permitted to enroll

   - Group 1 and DS patients with known non-hematopoietic, non-CNS/testicular
   extramedullary disease (i.e., chloromatous disease) are not eligible

      - Note: Group 2 and 3 patients with known non-hematopoietic, non-CNS/testicular
      extramedullary disease (i.e., chloromatous disease) are eligible if this is NOT
      the only site of relapsed disease

   - Female patients of childbearing potential are not eligible unless a negative pregnancy
   test result has been obtained within 7 days prior to enrollment. Patients who are
   sexually active and of reproductive potential are not eligible unless they agree to
   use an effective contraceptive method for the duration of this study. Men with female
   partners of childbearing potential should use effective contraception during the
   duration of their treatment. The effect of blinatumomab on fertility has not been
   evaluated. Blinatumomab is not recommended for pregnant women or women of childbearing
   potential (WOCBP) not using contraception. Females of reproductive potential must use
   effective contraception during treatment and for at least 48 hours after the last dose
   of blinatumomab. Studies in animal models have shown that nivolumab can adversely
   impair pregnancy. Thus, nivolumab is expected to cause fetal harm during pregnancy.
   WOCBP receiving nivolumab must continue contraception for a period of at least 5
   months after the last dose of nivolumab. It is unknown whether nivolumab is present in
   breast milk, thus breastfeeding should be discontinued while a patient is receiving
   nivolumab. Men receiving nivolumab and who are sexually active with WOCBP must
   continue contraception for 7 months after the last dose of nivolumab

   - Lactating females are not eligible unless they agree not to breastfeed their infants.
   It is unknown whether blinatumomab or its metabolites are excreted in human breast
   milk. Women are not permitted to breastfeed while receiving blinatumomab and for the
   last 48 hours after the last blinatumomab dose. Due to the potential for serious
   adverse reactions in the breastfed infant, women are not permitted to breastfeed
   during treatment and for 5 months after the last nivolumab dose