PRIMARY OBJECTIVES:

      I. To compare rate of minimal residual disease (MRD) negative second remission (Rem-2) after
      up to two cycles of reinduction with blinatumomab versus (vs.) blinatumomab/nivolumab in
      Group 1 patients aged >= 1 to < 31 years old with first relapse of CD19+ B-ALL.

      II. To compare event-free survival (EFS) PI (EFS post-induction) between consolidation with
      blinatumomab vs. blinatumomab/nivolumab in Group 3 patients aged >= 1 to <31 years old with
      first relapse of CD19+ B ALL.

      SECONDARY OBJECTIVES:

      I. To evaluate the safety and tolerability of blinatumomab/nivolumab in patients aged >= 1 to
      < 31 years old with first relapse of CD19+ B ALL.

      II. To compare EFS post-induction between blinatumomab vs. blinatumomab/nivolumab in Group 2
      patients aged >= 1 to < 31 years old with first relapse of CD19+ B ALL.

      EXPLORATORY OBJECTIVES:

      I. In Group 1 patients, compare EFS between blinatumomab monotherapy and
      blinatumomab/nivolumab arms as compared to similar patients treated on the predecessor trial
      AALL1331.

      II. In Group 1 patients, compare toxicity as defined by grade 3 or greater adverse events
      during the first cycle of blinatumomab or blinatumomab/nivolumab to similar patients treated
      with block 1 of cytotoxic chemotherapy on the predecessor trial AALL1331.

      III. In Group 2 patients with MRD >= 0.1% after vincristine sulfate, dexamethasone, pegylated
      asparaginase, and doxorubicin hydrochloride (VXLD), compare MRD negative second remission
      (Rem-2) rate after the first cycle of immunotherapy between blinatumomab monotherapy and
      blinatumomab/nivolumab arms.

      IV. In patients with Down syndrome (DS) with first relapse of B-ALL, describe the safety,
      tolerability and efficacy (as defined by MRD negative second remission, Rem-2) after up to
      two cycles of blinatumomab/nivolumab.

      OUTLINE: Patients >= 18 years old with marrow +/- extramedullary (EM) relapse of any duration
      after initial diagnosis, or patients < 18 years old with marrow +/- EM relapse < 24 months
      after initial diagnosis are assigned to Group 1. Patients < 18 years old with marrow +/- EM
      relapse >= 24 months from initial diagnosis, or all isolated extramedullary (IEM) relapses >=
      1 to < 31 years old are assigned to Groups 2-3 re-induction. Patients with DS are assigned to
      Arm G. NOTE: Patients in Group 1 and DS patients with white blood cells (WBC) >= 30,000/uL,
      CNS 2/3 disease, or testicular disease must first receive 1 of 3 pre-immunotherapy
      treatments.

      PRE-IMMUNOTHERAPY TREATMENT FOR PATIENTS WITH WBC >= 30,000/uL: Patients receive methotrexate
      (MTX) intrathecally (IT) or cytarabine IT or intrathecal triple therapy (ITT) consisting of
      MTX, hydrocortisone sodium succinate, and cytarabine IT at the time of diagnostic lumbar
      puncture (LP) or on day 1 (if intrathecal therapy is given with relapse diagnostic LP < 7
      days prior to the start of protocol therapy). Patients also receive dexamethasone
      intravenously (IV) or orally (PO) twice daily (BID) on days 1-5, vincristine sulfate IV push
      over 1 minute or via infusion on day 1. Patients with DS also receive leucovorin calcium PO
      or IV every 6 hours (q6h) for 2 doses on day 2 or at 24 and 30 hours after each MTX or ITT
      dose. Patients should proceed to the next cycle when CNS 1 and no testicular disease is
      present, no sooner than Day 8 and no later than Day 15.

      PRE-IMMUNOTHERAPY TREATMENT FOR CNS 2/3 DISEASE: Patients receive MTX IT or cytarabine IT
      twice weekly (Q2W) for 5-7 doses or Intrathecal Triple Therapy (ITT) IT Q2W for 3-4 doses
      until patient is CNS 1. Patients with DS also receive leucovorin calcium PO or IV q6h for 2
      doses at 24 and 30 hours after each MTX or ITT dose. Patients should proceed to the next
      cycle when CNS 1 and no testicular disease is present, no sooner than Day 15 and no later
      than Day 24.

      PRE-IMMUNOTHERAPY TREATMENT FOR TESTICULAR DISEASE: Patients receive MTX IT, cytarabine IT,
      or ITT IT on days 1 and 15 (day 1 may be omitted if intrathecal therapy is given with relapse
      diagnostic LP < 7 days prior to the start of protocol therapy). Patients with DS also receive
      leucovorin calcium PO or IV q6h for 2 doses on days 2 and 16 or at 24 and 30 hours after each
      IT MTX or ITT dose. Males with testicular disease at relapse undergo radiation once daily
      (QD) for a total of 12 fractions over 12 days. Patients should proceed to the next cycle when
      CNS 1 and no testicular disease is present, no sooner than Day 15 and no later than Day 22.

      GROUP 1: Patients are randomized to Arm A or Arm B.

      ARM A: Patients receive dexamethasone PO or IV on days 1 and 8 of cycle 1, blinatumomab via
      continuous IV infusion on days 1-28 of cycles 1-2, MTX IT, cytarabine IT, or ITT IT on days 1
      and 15 of cycle 1 (MTX on day 1 may be omitted if intrathecal therapy is given with relapse
      diagnostic LP < 7 days prior to the start of protocol therapy), and MTX IT on days 1 and 15
      of cycle 2. Treatment repeats every 36 days for 2 cycles in the absence of disease
      progression or unacceptable toxicity. NOTE: Patients with MRD < 0.01% after cycle 1 may stop
      study treatment or may choose to continue to cycle 2. Patients with MRD >= 0.01% after cycle
      1 proceed to cycle 2.

      ARM B: Patients receive dexamethasone, blinatumomab, and MTX, cytarabine, or ITT as in Arm A.
      Patients also receive nivolumab IV over 30 minutes on days 11 and 25 of cycle 1 and days 1
      and 15 of cycle 2. Treatment repeats every 36 days for 2 cycles in the absence of disease
      progression or unacceptable toxicity. NOTE: Patients with MRD < 0.01% after cycle 1 may stop
      study treatment or may choose to continue to cycle 2. Patients with MRD >= 0.01% after cycle
      1 proceed to cycle 2.

      GROUPS 2-3 REINDUCTION: Patients receive vincristine sulfate IV push over 1 minute or via
      infusion on days 1, 8, 15, and 22, dexamethasone PO or IV on days 1-14, doxorubicin
      hydrochloride IV over 1-15 minutes on day 1, MTX IT on days 1, 8, and 29 (day 1 may be
      omitted if intrathecal therapy is given with relapse diagnostic LP < 7 days prior to the
      start of protocol therapy) (days 8 and 29 for CNS 1/2 patients at relapse only), pegaspargase
      intramuscularly (IM) or IV over 1-2 hours on days 2 and 16, cytarabine IT on days 4 and 11
      (CNS 2 patients at relapse only), then Q2W until 3 consecutive samples are clear of blasts,
      and ITT IT on days 8, 15, 22, and 29 (CNS 3 patients at relapse only). Treatment continues in
      the absence of disease progression or unacceptable toxicity.

      GROUP 2: The following patients are randomized to Arm C or Arm D: 1) >= 1 to < 31 years old,
      IEM relapse < 18 months from diagnosis, regardless of MRD after Re-Induction. 2) < 18 years
      old with marrow relapse >= 24 to < 36 months from diagnosis regardless of MRD after
      Re-Induction, 3) >= 1 to < 31 years old, IEM relapse >= 18 months, and MRD >= 0.1% after
      Re-Induction, 4) < 18 years old with marrow relapse >= 36 months, and MRD >= 0.1% after
      Re-Induction.

      ARM C: Patients receive dexamethasone PO or IV on day 1 of cycle 1, blinatumomab via
      continuous IV infusion on days 1-28 of cycles 1 and 2, and MTX IT on days 1 and 15 of cycles
      1 and 2 (day 1 may be omitted from cycle 1 if intrathecal MTX is given < 7 days prior to the
      start of cycle 1 ). Treatment repeats every 36 days for 2 cycles in the absence of disease
      progression or unacceptable toxicity. NOTE: Patients with MRD < 0.01% after cycle 1 may stop
      study treatment or may choose to continue to cycle 2. Patients with MRD >= 0.01% after cycle
      1 proceed to cycle 2.

      ARM D: Patients receive dexamethasone, blinatumomab, and MTX as in Arm C. Patients also
      receive nivolumab IV over 30 minutes on days 11 and 25 of cycle 1 and days 1 and 15 of cycle
      2. Treatment repeats every 36 days for 2 cycles in the absence of disease progression or
      unacceptable toxicity. NOTE: Patients with MRD < 0.01% after cycle 1 may stop study treatment
      or may choose to continue to cycle 2. Patients with MRD >= 0.01% after cycle 1 proceed to
      cycle 2.

      GROUP 3: The following patients are randomized to Arm E or Arm F: 1) >= 1 to < 31 years old
      with IEM relapse >= 18 months from diagnosis and MRD < 0.1% after Re-Induction, 2) < 18 years
      old with marrow relapse >= 36 months from diagnosis and MRD < 0.1% after Re-Induction.

      ARM E:

      IMMUNOTHERAPY CYCLES 1-2: Patients receive dexamethasone PO or IV on day 1 of cycle 1 only,
      blinatumomab IV via continuous infusion on days 1-28, and MTX IT on days 1 and 15 (day 1 may
      be omitted from cycle 1 if intrathecal therapy is given < 7 days prior to the start of this
      cycle).Immunotherapy Cycles 1-2 alternate with Continuation Cycles 1-2.

      CONTINUATION CYCLES 1-2: Patients receive dexamethasone PO on days 1-5, vincristine sulfate
      IV push over 1 minute or via infusion on day 1, mercaptopurine PO on days 1-42, MTX PO on
      days 8, 15, 29, and 36, cyclophosphamide IV over 15-30 minutes on days 43 and 50, etoposide
      IV over 90-120 minutes on days 43 and 50, thioguanine PO once daily (QD) on days 43-49, and
      cytarabine IV over 1-30 minutes or subcutaneously (SC) on days 44-47 and 51-54. CNS 1/2
      patients at relapse also receive MTX IT on days 1 and 43 and PO q6h for 4 doses on day 22,
      and leucovorin calcium PO q6h for 2 doses on day 24. CNS 3 patients at relapse also receive
      ITT IT on days 1 and 43, intermediate dose MTX IV over 36 hours on day 22, and leucovorin
      calcium IV or PO q6h on days 24 and 25. Treatment repeats every 8 weeks for 2 cycles in the
      absence of disease progression or unacceptable toxicity.

      IMMUNOTHERAPY CYCLE 3: Patients receive blinatumomab IV via continuous infusion on days 1-28,
      and MTX IT on days 1 and 15.

      MAINTENANCE: Patients receive dexamethasone PO BID on days 1-5, 29-33, and 57-61, vincristine
      sulfate IV push over 1 minute or via infusion on days 1, 29, and 57, mercaptopurine PO on
      days 1-84, MTX IT on day 1 (CNS 1/2 patients at relapse only), ITT IT on day 1 (CNS 3
      patients at relapse only), and MTX PO on days 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, and 78.
      Treatment repeats every 12 weeks for 2 years from the start of Re-Induction therapy in the
      absence of disease progression or unacceptable toxicity.

      MAINTENANCE CHEMORADIATION (FOR CNS 3 PATIENTS ONLY): Beginning between the first and second
      cycles of maintenance therapy, patients receive dexamethasone PO BID on days 1-7 and 15-21,
      vincristine sulfate IV push over 1 minute or via infusion on days 1, 8, and 15, and
      pegaspargase IM or IV over 1-2 hours on day 1. Patients with CNS 3 and isolated CNS relapse
      undergo cranial radiation in the form of 3-dimensional (D)-conformal radiation therapy (CRT)
      over 5 days per week for a total of 10 treatments.

      ARM F:

      IMMUNOTHERAPY CYCLES 1-2: Patients receive dexamethasone PO or IV on day 1 of cycle 1 only,
      blinatumomab IV via continuous infusion on days 1-28, nivolumab IV over 30 minutes on days
      11-25 of cycle 1 and on days 1 and 15 of cycles 2 and 3, and MTX IT on days 1 and 15 (day 1
      may be omitted from cycle 1 if intrathecal therapy is given with < 7 days prior to the start
      of this cycle). Immunotherapy Cycles 1-2 alternate with Continuation Cycles 1-2.

      CONTINUATION CYCLES 1-2: Patients receive dexamethasone PO on days 1-5, vincristine sulfate
      IV push over 1 minute or via infusion on day 1, mercaptopurine PO on days 1-42, MTX PO on
      days 8, 15, 29, and 36, cyclophosphamide IV over 15-30 minutes on days 43 and 50, etoposide
      IV over 90-120 minutes on days 43 and 50, thioguanine PO QD on days 43-49, and cytarabine IV
      over 1-30 minutes or SC on days 44-47 and 51-54. CNS 1/2 patients at relapse also receive MTX
      IT on days 1 and 43 and PO q6h for 4 doses on day 22, and leucovorin calcium PO q6h for 2
      doses on day 24. CNS 3 patients at relapse also receive ITT IT on days 1 and 43, intermediate
      dose MTX IV over 36 hours on day 22, and leucovorin calcium IV or PO q6h on days 24 and 25.

      IMMUNOTHERAPY CYCLE 3: Patients receive blinatumomab IV via continuous infusion on days 1-28,
      nivolumab IV over 30 minutes on days 1 and 15 and MTX IT on days 1 and 15.

      MAINTENANCE: Patients receive dexamethasone PO BID on days 1-5, 29-33, and 57-61, vincristine
      sulfate IV push over 1 minute or via infusion on days 1, 29, and 57, mercaptopurine PO on
      days 1-84, MTX IT on day 1 (CNS 1/2 patients at relapse only), ITT IT on day 1 (CNS 3
      patients at relapse only), and MTX PO on days 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78.
      Treatment repeats every 12 weeks for 2 years from the start of Re-Induction therapy in the
      absence of disease progression or unacceptable toxicity.

      MAINTENANCE CHEMORADIATION (FOR CNS 3 PATIENTS): Beginning between the first and second
      cycles of maintenance therapy, patients receive dexamethasone PO BID on days 1-7 and 15-21,
      vincristine sulfate IV push over 1 minute or via infusion on days 1, 8, and 15, and
      pegaspargase IM or IV over 1-2 hours on day 1. Patients with CNS 3 and isolated CNS relapse
      undergo cranial radiation in the form of 3D-CRT over 5 days per week for a total of 10
      treatments in the absence of disease progression or unacceptable toxicity.

      ARM G (DS PATIENTS): Patients receive dexamethasone PO or IV on days 1 and 8 of cycle 1 only,
      blinatumomab IV via continuous infusion on days 1-28, nivolumab IV over 30 minutes on days 11
      and 25 of cycle 1 and days 1 and 15 of cycle 2, and MTX IT, cytarabine IT, or ITT IT on days
      1 and 15 of cycle 1 (MTX on day 1 may be omitted if intrathecal therapy is given with relapse
      diagnostic LP < 7 days prior to the start of protocol therapy), MTX IT on days 1 and 15 of
      cycle 2, and leucovorin calcium IV or PO q6h for 2 doses on days 2 and 16.

      Patients with MRD < 0.01% are eligible to come off protocol therapy to receive Consolidation
      therapy at the end of Cycle 1, or may choose to proceed to Arm G, Cycle 2.

      After completion of study treatment, patients are followed up every 3 months for 1 year.