Inclusion Criteria:

          -  PREREGISTRATION (STEP 0) ELIGIBILITY CRITERIA - INCLUSION

          -  Patient must be newly diagnosed with B-ALL or is suspected to have ALL

               -  Patient must have BCR-ABL1 positive disease. The diagnosis of ALL and the
                  presence of BCR-ABL translocation must be confirmed centrally. Patients can be
                  registered and begin Step 1 therapy while awaiting central laboratory eligibility
                  confirmation

                    -  NOTE: Bone marrow and/or peripheral blood specimen must be submitted to the
                       Eastern Cooperative Oncology Group-American College of Radiology Imaging
                       Network (ECOG-ACRIN) Leukemia Laboratory at MD Anderson Cancer Center to
                       determine patient's eligibility for registration to Step 1 or confirm
                       patient evaluability. Centrally fluorescence-activated cell sorting (FACS)
                       analysis will be performed to determine B-ALL and to exclude acute myeloid
                       leukemia (AML) or acute bi-phenotypic leukemia and baseline BCR-ABL status
                       will be determined by fluorescent in situ hybridization (FISH). The
                       ECOG-ACRIN Leukemia Laboratory will forward results within 48 hours of
                       receipt of the specimen to the submitting institution. Bone marrow is to be
                       from first pull (initial or re-direct). Specimens must contain sufficient
                       blast cells. In cases where the bone marrow aspiration may be inadequate, or
                       the bone marrow examination has already been performed prior to study
                       consent and enrollment on Step 0, peripheral blood may be submitted, given
                       that adequate circulating blasts are present (> 10%). If a diagnosis of
                       BCR-ABL positive B-ALL has already been established by local Clinical
                       Laboratory Improvement Act (CLIA) certified laboratories, the patient may be
                       registered to Step 1 without waiting for central confirmation

          -  Patients who started any kind of TKI prior to study registration are allowed to
             proceed on the study if they received no more than 14 days of TKI

          -  STEP 1 REGISTRATION ELIGIBILITY CRITERIA - INCLUSION

          -  The diagnosis of Philadelphia chromosome positive (Ph+) ALL has been determined
             locally, and bone marrow and/or peripheral blood was sent for central confirmation or
             determined centrally by the ECOG-ACRIN Leukemia Laboratory at MD Anderson Cancer
             Center

          -  Total bilirubin =< 3 mg/dL (unless related to Gilbert's syndrome in which case total
             bilirubin must be =< 5 mg/dL)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 X the institutional upper limit of normal (ULN)

          -  Estimated creatinine clearance > 45 mg/min (based on Cockcroft-Gault equation)

          -  Patients with acute organ dysfunction at registration, which may be attributed to
             leukemia can be registered regardless of lab results at presentation. Such patients
             will be allowed to register and can start Arm A steroid + TKI therapy but will only be
             allowed to proceed to Step 2 randomization if the eligibility criteria outlined is met

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial

          -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral
             load must be undetectable or on suppressive therapy, if indicated

          -  Patients with a history of hepatitis C virus (HCV) infection must have an undetectable
             HCV viral load and if indicated, on treatment

          -  Patients with a prior malignancy whose natural history or treatment does not have the
             potential to interfere with the safety or efficacy assessment of the investigational
             regimen are eligible for this trial

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients must be class 2B or better

          -  Investigators must confirm which TKI patient is to receive

               -  NOTE: Patients with known T315I mutation status should receive ponatinib
                  treatment

               -  NOTE: In situations due to insurance coverage issues and the pre-selected TKI is
                  not immediately available, patients can receive dasatinib or imatinib during Step
                  1. The investigator must re-specify dasatinib or ponatinib prior to Step 2
                  randomization and from then on patients must receive the pre-selected TKI only

          -  STEP 2: RANDOMIZATION - ELIGIBILITY CRITERIA - INCLUSION

          -  Patient must have completed at least 7 of 21 days of protocol-treatment on Arm A prior
             to randomization

               -  NOTE: First day of steroids prescription after registration will be considered as
                  the first day of study therapy. The selected TKI should be initiated prior to
                  randomization

          -  Patients who presented with acute organ dysfunction at Step 1 must have their total
             bilirubin and AST (SGOT)/ALT (SGPT) reduce to < 2 X institutional ULN and have an
             estimated creatinine clearance > 45 mg/min (based on Cockcroft-Gault equation)

          -  Investigators must confirm which TKI patient is to receive.

               -  NOTE: Patients with known T315I mutation status should receive ponatinib
                  treatment

          -  For patients under age 70, intended chemotherapy regimen must have been determined
             prior to randomization

          -  STEP 3: REGISTRATION (RE-INDUCTION) - ELIGIBILITY CRITERIA - INCLUSION

          -  Institution has received centralized MRD results confirming positive status

          -  Patients who presented with acute organ dysfunction must have their total bilirubin
             and AST (SGOT)/ALT (SGPT) reduce to < 2 X institutional ULN

          -  Patients who presented with acute organ dysfunction must have an estimated creatinine
             clearance > 45 mg/min (based on Cockcroft-Gault equation)

          -  Investigators must confirm which TKI patient is to receive

               -  NOTE: Patients with known T315I mutation status should receive ponatinib
                  treatment

          -  For patients under age 70 and previously assigned to Arm C, intended chemotherapy
             regimen must have been determined

        Exclusion Criteria:

          -  PREREGISTRATION (STEP 0) ELIGIBILITY CRITERIA - EXCLUSION

          -  Patient must not have received chemotherapy for B-ALL. Patients who received up to
             five days of hydroxyurea or steroids of any kind with the aim to reduce disease burden
             prior to study registration are eligible

          -  Patient must not have unstable epilepsy that requires treatment

          -  STEP 1 REGISTRATION ELIGIBILITY CRITERIA - EXCLUSION

          -  Women must not be pregnant or breast-feeding due to the potential harm to an unborn
             fetus and possible risk for adverse events in nursing infants with the treatment
             regimens being used. All females of childbearing potential must have a blood test or
             urine study within 14 days prior to registration to rule out pregnancy. A female of
             childbearing potential is defined as any woman, regardless of sexual orientation or
             whether they have undergone tubal ligation, who meets the following criteria: 1) has
             achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral
             oophorectomy, or 3) has not been naturally postmenopausal (amenorrhea following cancer
             therapy does not rule out childbearing potential) for at least 24 consecutive months
             (i.e., has had menses at any time in the preceding 24 consecutive months)

          -  Women of childbearing potential and sexually active males must not expect to conceive
             or father children by using accepted and effective method(s) of contraception or by
             abstaining from sexual intercourse from the time of registration, while on study
             treatment, and until at least six months after the last dose of study treatment

          -  Patient must not have active concomitant malignancy. Patients on chronic hormonal
             therapy for breast or prostate cancer or patients treated with maintenance with
             targeted agents but are in remission with no evidence for the primary malignancies can
             be included

          -  Patients must not have complaints of symptoms and/or have clinical and/or radiological
             signs that indicate an uncontrolled infection or any other concurrent medical
             condition that could be exacerbated by the treatment or would seriously complicate
             compliance with the protocol

          -  STEP 2: RANDOMIZATION - ELIGIBILITY CRITERIA - EXCLUSION

          -  Patient must not have active central nervous system (CNS) involvement by leukemic
             blasts. Patients with signs of CNS involvement at presentation are eligible for
             randomization if clearance of blasts from the cerebrospinal fluid (CSF) is
             demonstrated