PRIMARY OBJECTIVE:

      I. To determine in a randomized manner if the addition of 2 blocks of inotuzumab ozogamicin
      to modified Berlin-Frankfurt-Munster (mBFM) chemotherapy will improve 5-year disease-free
      survival (DFS) in children and young adults with high-risk B-cell acute lymphoblastic
      leukemia (HR B-ALL).

      SECONDARY OBJECTIVES:

      I. To describe the 5-year DFS for a favorable risk subset of National Cancer Institute (NCI)
      HR B-ALL (HR-Fav) when treated with mBFM chemotherapy with a single high-dose methotrexate
      (HD-MTX) interim maintenance (IM) phase and treatment duration of 2 years from the start of
      IM regardless of sex.

      II. To determine the toxicity and tolerability of inotuzumab ozogamicin integrated into the
      mBFM chemotherapy backbone in HR B-ALL.

      III. To describe the 5-year event-free survival (EFS) for patients with mixed phenotype acute
      leukemia (MPAL) receiving mBFM HR B-ALL therapy that includes a second IM phase with Capizzi
      intravenous (IV) methotrexate (MTX) without leucovorin rescue plus pegaspargase (C-MTX).

      IV. To describe the 5-year EFS for patients with disseminated (Murphy stage III-IV) B-cell
      lymphoblastic lymphoma (B-LLy) receiving mBFM HR B-ALL therapy that includes a second IM
      phase with C-MTX.

      EXPLORATORY OBJECTIVES:

      I. To describe the therapy administered, disease response, and survival outcomes of patients
      with MPAL who come off protocol therapy due to poor disease response to ALL therapy either
      during Induction, at end of induction (EOI), or at end of consolidation (EOC).

      II. To define the prevalence and significance of minimal marrow disease (MMD) at diagnosis
      and bone marrow minimal residual disease (MRD) at EOI in disseminated B-LLy.

      III. To determine the impact of proposed adherence-enhancing interventions on adherence to
      oral 6-mercaptopurine in patients with ALL.

      OUTLINE: All patients receive the same Induction and Consolidation chemotherapy. Patients
      with HR-Fav B-ALL are assigned to Arm I. Patients with HR B-ALL are randomized to Arm II or
      III. Patients with MPAL are assigned to Arm IV, and patients with B-LLy are assigned to Arm
      V.

      All patients with B-ALL receive Induction and Consolidation therapy:

      INDUCTION: Patients receive cytarabine intrathecally (IT) on day 1 and central nervous system
      (CNS)2 patients also receive cytarabine IT on days 4, 5 or 6 and 11 or 12. Patients also
      receive vincristine intravenously (IV) or IV push over 1 minute on days 1, 8, 15, and 22,
      daunorubicin IV over 1-15 minutes days 1, 8, 15, and 22, pegaspargase intramuscularly (IM) or
      IV over 1-2 hours on day 4, and methotrexate IT on days 8 and 29 (and on days 15 and 22 for
      CNS3 patients). Patients < 10 years old receive dexamethasone orally (PO) twice daily (BID)
      or IV on days 1-14; patients >= 10 years old receive prednis(ol)one PO BID or IV on days
      1-28. Treatment continues for 5 weeks in the absence of disease progression or unacceptable
      toxicity.

      CONSOLIDATION: Patients receive cyclophosphamide IV over 30-60 minutes on days 1 and 29,
      cytarabine IV over 1-30 minutes or subcutaneously (SC) on days 1-4, 8-11, 29-32, and 36-39,
      mercaptopurine PO once daily (QD) on days 1-14 and 29-42, and methotrexate IT on days 1, 8,
      15, and 22 (CNS3 patients receive methotrexate IT on days 1 and 8). Patients also receive
      vincristine IV or IV push over 1 minute on days 15, 22, 43, and 50, and pegaspargase IV over
      1-2 hours or IM on days 15 and 43. Treatment continues for 8 weeks in the absence of disease
      progression or unacceptable toxicity. Additionally, patients with testicular disease at
      diagnosis that does not resolve by the end of induction will undergo radiation therapy over
      12 once daily fractions.

      POST-CONSOLIDATION THERAPY: After Consolidation, based on clinical features and response,
      patients with B-ALL are designated as HR-Fav or HR B-ALL. Patients with HR-Fav B-ALL are
      assigned to Arm I. Patients with HR B-ALL are randomized to Arm II or III. Patients with MPAL
      and B-LLy are assigned to therapy arms (Arms IV and V) that are identical to Arm II. Patients
      that are < 10 years, have CNS1, no testicular leukemia, with favorable cytogenetics (ETV6
      RUNX1 fusion or double trisomies [4 and 10]), =< 24 hours of steroids in the two weeks prior
      to diagnosis, and EOI MRD < 0.01% are assigned to Arm I. Patients with HR B-ALL who are
      surface CD22 positive at diagnosis and have MRD < 0.01% by the end of Consolidation, are
      randomized to either Arm II or III.

      ARM I: HR-FAV B-ALL (Patients that are < 10 years, have CNS1 status, no testicular leukemia,
      with favorable cytogenetics (ETV6 RUNX1 fusion or double trisomies [4 and 10]), =< 24 hours
      of steroids in the two weeks prior to diagnosis, and EOI MRD < 0.01%)

      INTERIM MAINTENANCE: Patients receive vincristine IV or IV push over 1 minute on days 1, 15,
      29, and 43, high dose methotrexate IV over 24 hours on days 1, 15, 29, and 43, leucovorin PO
      or IV on days 3-4, 17-18, 31-32, and 45-46, mercaptopurine PO QD on days 1-14, 15-28, 29-42,
      and 43-56, and methotrexate IT on days 1 and 29. Treatment continues for 9 weeks in the
      absence of disease progression or unacceptable toxicity.

      DELAYED INTENSIFICATION (PART I): Patients receive methotrexate IT on day 1, dexamethasone PO
      BID or IV on days 1-7 and 15-21, vincristine IV or IV push over 1 minute on days 1, 8, and
      15, doxorubicin IV over 1-15 minutes or up to 1 hour on days 1, 8, and 15, and pegaspargase
      or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day 4. Treatment (Parts I and
      II of Delayed Intensification) continues for 8 weeks in the absence of disease progression or
      unacceptable toxicity. Calaspargase pegol can only be given to patients less than 21 years of
      age.

      DELAYED INTENSIFICATION (PART II): Patients receive cyclophosphamide IV over 30-60 minutes on
      day 29, thioguanine PO on days 29-42, cytarabine IV over 1-30 minutes or SC on days 29-32 and
      36-39, methotrexate IT on days 29 and 36, vincristine IV or IV push over 1 minute on days 43
      and 50, and pegaspargase or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day
      43. Treatment (Parts I and II of Delayed Intensification) continues for 8 weeks in the
      absence of disease progression or unacceptable toxicity. Calaspargase pegol can only be given
      to patients less than 21 years of age.

      MAINTENANCE: Patients receive methotrexate IT on days 1 and 29 for cycles 1-4, and day 1 for
      subsequent cycles. Patients also receive vincristine IV or IV push over 1 minute on day 1,
      prednisolone PO BID or IV on days 1-5, mercaptopurine PO QD on days 1-84, and methotrexate PO
      on days 8, 15, 22, (29 excluded in cycles 1-4), 36, 43, 50, 57, 64, 71, and 78. Cycles repeat
      every 12 weeks for up to 2 years in the absence of disease progression or unacceptable
      toxicity.

      Patients with HR B-ALL who have MRD < 0.01% by the end of Consolidation, and leukemic blasts
      positive for surface CD22 at diagnosis are randomized to Arm II or Arm III.

      ARM II: HR B-ALL (CONTROL) INTERIM MAINTENANCE I: Patients receive vincristine IV or IV push
      over 1 minute on days 1, 15, 29 and 43, high dose methotrexate IV over 24 hours on days 1,
      15, 29 and 43, leucovorin PO or IV on days 3-4, 17-18, 31-32, 45-46, mercaptopurine PO QD on
      days 1-14, 15-28, 29-42, and 43-56, and methotrexate IT on days 1 and 29. Treatment continues
      for 9 weeks in the absence of disease progression or unacceptable toxicity.

      DELAYED INTENSIFICATION (PART I): Patients receive methotrexate IT on day 1, dexamethasone PO
      BID or IV on days 1-7 and 15-21, vincristine IV or IV push over 1 minute on days 1, 8, and
      15, doxorubicin IV over 1-15 minutes or up to 1 hour on days 1, 8, and 15, and pegaspargase
      or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day 4. Treatment (Parts I and
      II of Delayed Intensification) continues for 8 weeks in the absence of disease progression or
      unacceptable toxicity. Calaspargase pegol can only be given to patients less than 21 years of
      age.

      DELAYED INTENSIFICATION (PART II): Patients receive cyclophosphamide IV over 30-60 minutes on
      day 29, thioguanine PO on days 29-42, cytarabine IV over 1-30 minutes or SC on days 29-32 and
      36-39, methotrexate IT on days 29 and 36, vincristine IV or IV push over 1 minute on days 43
      and 50, and pegaspargase or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day
      43. Treatment (Parts I and II of Delayed Intensification) continues for 8 weeks in the
      absence of disease progression or unacceptable toxicity. Calaspargase pegol can only be given
      to patients less than 21 years of age.

      INTERIM MAINTENANCE II: Patients receive vincristine IV or IV push over 1 minute on days 1,
      11, 21, 31 and 41, methotrexate IV over 2-15 minutes or 10-15 minutes on days 1, 11, 21, 31,
      and 41, methotrexate IT on days 1 and 31, and pegaspargase or calaspargase pegol IV over 1-2
      hours or pegaspargase IM on days 2 and 22. Treatment continues for 8 weeks in the absence of
      disease progression or unacceptable toxicity. Calaspargase pegol can only be given to
      patients less than 21 years of age.

      ARM III: HR B-ALL (EXPERIMENTAL) INOTUZUMAB OZOGAMICIN (InO) BLOCK 1: Patients receive
      inotuzumab ozogamicin IV over 60 minutes on days 1, 8, and 15 and methotrexate IT on day 1.
      Treatment continues for 4 weeks in the absence of disease progression or unacceptable
      toxicity.

      INTERIM MAINTENANCE I: Patients receive vincristine IV or IV push over 1 minute on days 1,
      15, 29 and 43, high dose methotrexate IV over 24 hours on days 1, 15, 29, and 43, leucovorin
      PO or IV on days 3-4, 17-18, 31-32, and 45-46, mercaptopurine PO on days 1-14, 15-28, 29-42,
      and 43-56, and methotrexate IT on days 1 and 29. Treatment continues for 9 weeks in the
      absence of disease progression or unacceptable toxicity.

      InO BLOCK 2: Patients receive inotuzumab ozogamicin IV over 60 minutes on days 1, 8, and 15.
      Treatment continues for 4 weeks in the absence of disease progression or unacceptable
      toxicity.

      DELAYED INTENSIFICATION (PART I): Patients receive methotrexate IT on day 1, dexamethasone PO
      BID or IV on days 1-7 and 15-21, vincristine IV or IV push over 1 minute on days 1, 8, and
      15, doxorubicin IV over 1-15 minutes or up to 1 hour on days 1, 8, and 15, and pegaspargase
      or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day 4. Treatment (Parts I and
      II of Delayed Intensification) continues for 8 weeks in the absence of disease progression or
      unacceptable toxicity. Calaspargase pegol can only be given to patients less than 21 years of
      age.

      DELAYED INTENSIFICATION (PART II): Patients receive cyclophosphamide IV over 30-60 minutes on
      day 29, thioguanine PO on days 29-42, cytarabine IV over 1-30 minutes or SC on days 29-32 and
      36-39, methotrexate IT on days 29 and 36, vincristine IV or IV push over 1 minute on days 43
      and 50, and pegaspargase or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day
      43. Treatment (Parts I and II of Delayed Intensification) continues for 8 weeks in the
      absence of disease progression or unacceptable toxicity. Calaspargase pegol can only be given
      to patients less than 21 years of age.

      INTERIM MAINTENANCE II: Patients receive vincristine IV or IV push over 1 minute on days 1,
      11, 21, 31, and 41, methotrexate IV on days 1, 11, 21, 31, and 41, methotrexate IT on days 1
      and 31, and pegaspargase or calaspargase pegol IV over 1-2 hours or pegaspargase IM on days 2
      and 22. Treatment continues for 8 weeks in the absence of disease progression or unacceptable
      toxicity. Calaspargase pegol can only be given to patients less than 21 years of age.

      ARMS II AND III: HR B-ALL MAINTENANCE: Patients receive vincristine IV or IV push over 1
      minute on day 1, prednisolone PO BID or IV on days 1-5, mercaptopurine PO on days 1-84,
      methotrexate PO on days 8, 15, 22, 29 (excluded in cycles 1 and 2), 36, 43, 50, 57, 64, 71
      and 78, and methotrexate IT on days 1 (and 29 of cycles 1-2 for patients who do not receive
      cranial radiation). Cycles repeat every 12 weeks for up to 2 years in the absence of disease
      progression or unacceptable toxicity. Patients with CNS3 disease undergo cranial radiation
      therapy over 10 fractions during the first 4 weeks.

      ARM IV: MPAL INDUCTION: Patients receive cytarabine IT on day 1 and CNS2 patients also
      receive cytarabine IT on days 4, 5 or 6 and 11 or 12. Patients also receive vincristine IV or
      IV push over 1 minute on days 1, 8, 15, and 22, daunorubicin IV over 1-15 minutes days 1, 8,
      15, and 22, pegaspargase IM or IV over 1-2 hours on day 4, and methotrexate IT on days 8 and
      29 (and on days 15 and 22 for CNS3 patients). Patients < 10 years old receive dexamethasone
      PO BID or IV on days 1-14; patients >= 10 years old receive prednisolone PO BID or IV on days
      1-28. Treatment continues for 5 weeks in the absence of disease progression or unacceptable
      toxicity.

      CONSOLIDATION: Patients receive cyclophosphamide IV over 30-60 minutes on days 1 and 29,
      cytarabine IV over 1-30 minutes or SC on days 1-4, 8-11, 29-32, and 36-39, mercaptopurine PO
      on days 1-14 and 29-42, methotrexate IT on days 1, 8, 15, and 22 (excluded on days 15 and 22
      for CNS3 patients), vincristine IV or IV push over 1 minute on days 15, 22, 43, and 50, and
      pegaspargase IV over 1-2 hours or IM on days 15 and 43. Treatment continues for 8 weeks in
      the absence of disease progression or unacceptable toxicity. Patients with testicular disease
      at diagnosis that does not resolve by the end of induction will and continued evidence of
      testicular disease at end of induction undergo testicular radiation over 12 once-daily
      fractions.

      ARM V: B-LLY INDUCTION: Patients receive cytarabine IT on day 1 and CNS2 patients also
      receive cytarabine IT on days 4, 5 or 6 and 11 or 12. Patients also receive vincristine IV or
      IV push over 1 minute on days 1, 8, 15, and 22, daunorubicin IV over 1-15 minutes days 1, 8,
      15, and 22, pegaspargase IM or IV over 1-2 hours on day 4, and methotrexate IT on days 8 and
      29 (and on days 15 and 22 for CNS3 patients). Patients < 10 years old receive dexamethasone
      PO BID or IV on days 1-14; patients >= 10 years old receive prednisolone PO BID or IV on days
      1-28. Treatment continues for 5 weeks in the absence of disease progression or unacceptable
      toxicity.

      CONSOLIDATION: Patients receive cyclophosphamide IV over 30-60 minutes on days 1 and 29,
      cytarabine IV over 1-30 minutes or SC on days 1-4, 8-11, 29-32, and 36-39, mercaptopurine PO
      on days 1-14 and 29-42, methotrexate IT on days 1, 8, 15, and 22 (excluded on days 15 and 22
      CNS3 patients), vincristine IV or IV push over 1 minute on days 15, 22, 43, and 50, and
      pegaspargase IV over 1-2 hours or IM on days 15 and 43. Treatment continues for 8 weeks in
      the absence of disease progression or unacceptable toxicity. Patients with testicular disease
      at diagnosis that does not resolve by the end of induction will and continued evidence of
      testicular disease at end of induction undergo testicular radiation therapy over 12
      once-daily fractions.

      ARM IV AND V: MPAL AND B-LLY (Post-Consolidation Therapy) INTERIM MAINTENANCE I: Patients
      receive vincristine IV or IV push over 1 minute on days 1, 15, 29, and 43, high dose
      methotrexate IV over 24 hours on days 1, 15, 29, and 43, leucovorin PO or IV on days 3-4,
      17-18, 31-32, and 45-46, methotrexate IT on days 1 and 29 and mercaptopurine PO QD on days
      1-14, 15-28, 29-42, and 43-56. Treatment continues for 9 weeks in the absence of disease
      progression or unacceptable toxicity.

      DELAYED INTENSIFICATION (PART I): Patients receive methotrexate IT on day 1, dexamethasone PO
      BID or IV on days 1-7 and 15-21, vincristine IV or IV push over 1 minute on days 1, 8, and
      15, doxorubicin IV over 1-15 minutes or up to 1 hour on days 1, 8, and 15, and pegaspargase
      or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day 4. Treatment (Parts I and
      II of Delayed Intensification) continues for 8 weeks in the absence of disease progression or
      unacceptable toxicity. Calaspargase pegol can only be given to patients less than 21 years of
      age.

      DELAYED INTENSIFICATION (PART II): Patients receive cyclophosphamide IV over 30-60 minutes on
      day 29, thioguanine PO on days 29-42, cytarabine IV over 1-30 minutes or SC on days 29-32 and
      36-39, methotrexate IT on days 29 and 36, vincristine IV or IV push over 1 minute on days 43
      and 50, and pegaspargase or calaspargase pegol IV over 1-2 hours or pegaspargase IM on day
      43. Treatment (Parts I and II of Delayed Intensification) continues for 8 weeks in the
      absence of disease progression or unacceptable toxicity. Calaspargase pegol can only be given
      to patients less than 21 years of age.

      INTERIM MAINTENANCE II: Patients receive vincristine IV or IV push over 1 minute on days 1,
      11, 21, 31, and 41, methotrexate IV or infusion over 2-15 minutes or 10-15 minutes on days 1,
      11, 21, 31, and 41, methotrexate IT on days 1 and 31, and pegaspargase or calaspargase pegol
      IV over 1-2 hours or pegaspargase IM on days 2 and 22. Treatment continues for 8 weeks in the
      absence of disease progression or unacceptable toxicity. Calaspargase pegol can only be given
      to patients less than 21 years of age.

      MAINTENANCE: Patients receive vincristine IV or IV push over 1 minute on days 1, prednisolone
      PO BID or IV on days 1-5, mercaptopurine PO on days 1-84, methotrexate PO on days 8, 15, 22,
      29 (excluded in cycles 1 and 2), 36, 43, 50, 57, 64, 71, and 78, and methotrexate IT on days
      1 (and 29 of cycles 1-2 for patients who do not receive cranial radiation). Cycles repeat
      every 12 weeks for up to 2 years in the absence of disease progression or unacceptable
      toxicity. Patients with CNS3 disease at diagnosis undergo cranial radiation therapy for 10
      fractions over 4 weeks.

      After completion of study treatment, patients are followed up at 4 weeks, then every 3 months
      for 2 years, every 4-6 months for the third year, then every 6-12 months for years 4-5.