Inclusion Criteria:

          -  PRE-REGISTRATION

          -  Diagnostic bone marrow and peripheral blood specimens must be submitted for
             immunophenotyping and selected molecular testing, and the establishment of BCR/ABL
             status; testing will be performed by the Eastern Cooperative Oncology Group
             (ECOG)-American College of Radiation Imaging Network (ACRIN) Leukemia Translational
             Research Laboratory (LTRL) and reported to the institution

               -  NOTE: IT IS ESSENTIAL THAT A SAMPLE CONTAINING SUFFICIENT BLAST CELLS BE
                  SUBMITTED TO THE ECOG-ACRIN LTRL AT BASELINE SO THAT SUBSEQUENT BONE MARROW
                  ASSESSMENTS OF MRD CAN BE DONE; IN ADDITION TO ALLOWING THE LTRL TO CONFIRM
                  ELIGIBILITY BASED ON BLAST CELL IMMUNOPHENOTYPE AND BCR/ABL STATUS, IT IS ALSO
                  IMPERATIVE THAT AN ADEQUATE NUMBER OF BLASTS BE BANKED FOR ANALYSIS BY DRS
                  MULLIGHAN/WILLMAN. WITHOUT ADEQUATE BASELINE SAMPLES, PATIENTS WILL NOT BE ABLE
                  TO BE TREATED AND RANDOMIZED ON THIS PROTOCOL; IF A BONE MARROW ASPIRATE IS NOT
                  AVAILABLE FOR LTRL SUBMISSION AT BASELINE, IT IS IMPERATIVE THAT DR PAIETTA FROM
                  THE LTRL IS CALLED TO DISCUSS THE PERIPHERAL BLOOD WBC AND BLAST COUNT BEFORE
                  BLOOD ONLY IS SUBMITTED

               -  NOTE: Hydroxyurea can be given for up to 5 days prior to initiation of protocol
                  therapy for control of leukocyte count and/or other symptoms or signs;
                  corticosteroids can be given after pre-registration to the protocol and
                  submission of baseline marrow and blood samples for control of leukocyte count
                  and/or other symptoms or signs prior to initiation of protocol therapy if needed;
                  if corticosteroids are given prior to pre-registration, contact the study chair
                  as the patient may still be eligible to participate

          -  INDUCTION ELIGIBILITY CRITERIA-STEP 1

          -  New diagnosis of B lineage ALL must be made upon bone marrow or peripheral blood
             immunophenotyping; cases with myeloid antigen expression, but unequivocal lymphoid
             immunophenotype, are eligible

          -  Negativity for the Philadelphia chromosome must be established by conventional
             cytogenetics, fluorescence in situ hybridization (FISH) and/or polymerase chain
             reaction (PCR); patients who are negative for the Philadelphia chromosome by
             conventional cytogenetics must have FISH or PCR performed for BCR/ABL to exclude
             occult translocations

          -  Cytogenetic analysis must be performed from diagnostic bone marrow (preferred) or if
             adequate number of circulating blasts from peripheral blood; FISH testing for common
             B-lineage ALL abnormalities including t(9;22) (BCR/ABL1), t(12;21) (ETS-variant gene 6
             [ETV6]/runt-related transcription factor 1 [RUNX1]), t(1;19) (pre-B-cell leukemia
             homeobox 1 [PBX1]/transcription factor 3 [TCF3]), +4,+10,+17, (centromeric
             [Cen]4/Cen10/Cen17), t(11q23;var), (myeloid/lymphoid or mixed lineage leukemia [MLL]),
             deletion (del)(9p) (cyclin-dependent kinase inhibitor 2A [CDKN2A]/Cen9), and t(14;var)
             (immunoglobulin heavy chain [IGH] is encouraged); if there are few or no circulating
             blasts and an adequate marrow sample cannot be obtained for cytogenetic analysis, the
             patient may still enroll on the trial

          -  Serum direct bilirubin < 2 mg/dl or serum total bilirubin =< 3 (obtained =< 48 hours
             prior to registration); NOTE: the above stipulation for normal hepatic function does
             not apply if liver dysfunction is due to leukemia infiltration

          -  Serum creatinine < 2 mg/dl (obtained =< 48 hours prior to registration); NOTE: the
             above stipulation for normal hepatic function does not apply if liver dysfunction is
             due to leukemia infiltration

          -  Patient should be human leukocyte antigen (HLA) typed (A, B, C, DR and DQ) during
             induction therapy phase or a written explanation for not undergoing HLA typing on the
             flow sheet

          -  Patients with known human immunodeficiency virus (HIV) infection are eligible if they
             meet all of the following criteria:

               -  No history of acquired immune deficiency syndrome (AIDS)-related complications
                  other than a history of low CD4+ T-cell count (< 200/mm^3) prior to initiation of
                  combination antiretroviral therapy; on study CD4+ T-cell count may not be
                  informative due to leukemia and should not be used as an exclusion criterion if
                  low

               -  Patient must be healthy on the basis of HIV disease with high likelihood of near
                  normal life span were it not for the leukemia

               -  Patient must have serum HIV viral load of < 200 copies/mm^3

               -  Patient must be on combination antiretroviral therapy with minimal
                  pharmacokinetic interactions with study therapy and minimal overlapping clinical
                  toxicity with protocol therapy

               -  Patient must not be receiving protease inhibitors or once daily formulations
                  containing cobicistat, stavudine, or on regimens containing stavudine or
                  zidovudine

               -  It is recommended to utilize a regimen of the integrase inhibitor, dolutegravir,
                  combined with either disoproxil fumarate/emtricitabine or dolutegravir combined
                  with tenofovir alafenamide/emtricitabine

          -  Patient must not have an antecedent hematologic disorder

          -  Patient must have no history of recent myocardial infarction (within three months),
             uncontrolled congestive heart failure, or uncontrolled cardiac arrhythmia

          -  Patient must not have a history or presence of clinically relevant central nervous
             system (CNS) pathology such as epilepsy, seizure, paresis, aphasia, stroke, severe
             brain injuries, dementia; Parkinson's disease, cerebellar disease, organic brain
             syndrome, psychosis, or other significant CNS abnormalities

          -  Patient must have a normal cardiac ejection fraction by pretreatment multigated
             acquisition scan (MUGA) or echocardiogram within 4 weeks prior to registration
             (resting ejection fraction >= 40% or >= 5% increase with exercise), shortening
             fraction by echocardiogram >= 24%, or to within the normal range of values for the
             institution

          -  Patient must not have an active uncontrolled infection

          -  Women must not be pregnant or breast-feeding and must not become pregnant or
             breastfeed during protocol therapy and for at least 3 months after protocol therapy;
             woman of childbearing potential must abstain from sexual activity or be willing to use
             2 highly effective forms of contraception throughout protocol therapy and for at least
             an additional 3 months after the last dose of protocol-specified therapy; all females
             of childbearing potential must have a blood test or urine study within 2 weeks prior
             to registration to rule out pregnancy; a female of childbearing potential is any
             woman, regardless of sexual orientation or whether they have undergone tubal ligation,
             who meets the following criteria: has not undergone a hysterectomy or bilateral
             oophorectomy; or has not been naturally postmenopausal for at least 24 consecutive
             months (i.e., has had menses at any time in the preceding 24 consecutive months)

          -  Men who have a female partner of childbearing potential must be willing to use 2
             highly effective forms of contraception throughout protocol therapy and for at least
             an additional 3 months after the last dose of protocol-specified therapy; men who have
             a pregnant partner must be willing to use a condom during sexual activity throughout
             protocol therapy and for 3 months after the last dose of protocol-specified therapy

          -  ECOG performance score 0-3

          -  Patient must have given written informed consent

          -  POST-INDUCTION THERAPY ELIGIBILITY CRITERIA (PRIOR TO INTENSIFICATION-STEP 2)

          -  ECOG performance status 0-2

          -  Patients must have achieved a CR or CRi

          -  Patients who have achieved a CR or CRi must have maintained peripheral blood evidence
             of a CR or CRi

          -  Patient must be CNS (cerebrospinal fluid [CSF]) negative for leukemia

          -  Patients must have resolved any serious infectious complications related to induction

          -  Any significant medical complications related to induction must have resolved

          -  Serum creatinine =< 2.0 mg/dl (obtained =< 48 hours prior to registration)

          -  Serum direct bilirubin < 2 mg/dL or serum total bilirubin =< 3 (obtained =< 48 hours
             prior to registration)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) < 3 x upper limit
             of normal (ULN) (obtained =< 48 hours prior to registration)

          -  RANDOMIZATION OR ASSIGNMENT TO BLINATUMOMAB OR NO BLINATUMOMAB-STEP 3

          -  Patients must have an ECOG performance status of 0-2

          -  Patients must have maintained peripheral blood evidence of a remission and must have a
             CR or CRi, confirmed on restaging bone marrow (BM) aspirate and biopsy

          -  Patients must have resolved any serious infectious complications related to therapy

          -  Any significant medical complications related to therapy must have resolved

          -  Direct or total bilirubin < 1.5 x ULN (unless related to Gilbert's or Meulengracht's
             syndrome); the values must be obtained within 48 hours prior to randomization

          -  Serum creatinine < 1.5 x ULN; the values must be obtained within 48 hours prior to
             randomization

          -  Bone marrow aspirates must be submitted for centralized minimal residual disease (MRD)
             assessment performed by the ECOG-ACRIN Leukemia Translational Research Laboratory

          -  MRD results will be reported to the submitting institution

               -  NOTE: FOR MRD ASSESSMENTS, AN ASPIRATE FROM A SEPARATE BONE MARROW ASPIRATION
                  SITE MUST BE SUBMITTED (THE NEEDLE CAN BE RE-DIRECTED THROUGH THE SAME SKIN
                  PUNCTURE SITE); ONLY SUBMIT ASPIRATES FROM THE FIRST PULL OF AN ASPIRATION SITE
                  FOR MRD TESTING; DO NOT SUBMIT SAMPLES FROM THE SECOND OR THIRD PULL OF THE SAME
                  ASPIRATION SITE

               -  In B-lineage ALL, MRD levels in peripheral blood or from a dilute marrow
                  aspiration can be 300% lower, on average, than those in bone marrow at a given
                  time point; submitting a first pull from a separate aspiration site will ensure
                  that MRD determinations used in randomization and trial interpretation are
                  accurate

                    -  NOTE: failure to submit bone marrow aspirates will result in a major
                       violation at the time of an audit

          -  CRITERIA FOR ALLOGENEIC TRANSPLANTATION

          -  A suitable donor must be identified; there are no restrictions on donor type and can
             include a matched sibling, a matched or mismatched unrelated donor, a family haplotype
             matched donor or a cord blood donor (single or double)

          -  Patients should meet the eligibility criteria for RANDOMIZATION OR ASSIGNMENT TO
             BLINATUMOMAB OR NO BLINATUMOMAB-STEP 3

          -  Patients must be considered reliable enough to comply with the medication regimen and
             follow-up, and have social support necessary to allow this compliance

          -  CRITERIA FOR MAINTENANCE THERAPY-STEP 4: Patients must have an ECOG performance status
             of 0-3

          -  CRITERIA FOR MAINTENANCE THERAPY-STEP 4: Patients must have maintained peripheral
             blood evidence of a remission and must have a CR or CRi, confirmed on restaging BM
             aspirate and biopsy

          -  CRITERIA FOR MAINTENANCE THERAPY-STEP 4: Patients must have resolved any serious
             infectious complications related to therapy

          -  CRITERIA FOR MAINTENANCE THERAPY-STEP 4: Any significant medical complications related
             to therapy must have resolved

        Exclusion Criteria:

          -  Mature B ALL (Burkitt's-like leukemia) is excluded from enrollment in this trial;
             pre-study bone marrow biopsy and aspirate must be completed =< 1 week prior to
             registration

          -  Patient must not have a concurrent active malignancy for which they are receiving
             treatment

          -  Patient must not have intercurrent organ damage or medical problems that will
             jeopardize the outcome of therapy (i.e., psychiatric disorder, drug abuse, pregnancy)