Inotuzumab Ozogamicin and Frontline Chemotherapy in Treating Young Adults With Newly Diagnosed B Acute Lymphoblastic Leukemia

Inclusion Criteria: REGISTRATION ELIGIBILITY CRITERIA (STEP 1) * Newly diagnosed patients with CD-22 positive B-cell acute lymphoblastic leukemia (WHO criteria) are eligible. Patients with Burkitt type ALL are NOT eligible * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Single-dose intrathecal cytarabine is allowed prior to registration or prior to initiation of systematic therapy for patient convenience; this is usually done at the time of the diagnostic bone marrow or venous line placement to avoid a second lumbar puncture; systemic chemotherapy must begin within 72 hours of this intrathecal therapy * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Age \>= 18 years and \< 40 years * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN), unless suspected leukemic involvement of the liver * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Direct bilirubin =\< 3 x upper limit of normal (ULN), unless suspected leukemic involvement of the liver * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Calculated (calc.) creatinine clearance \>= 50 mL/min by Cockcroft-Gault * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) CONFIRMATION OF TOLERABILITY AND PHASE III ONLY): Completion of remission induction therapy * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) CONFIRMATION OF TOLERABILITY AND PHASE III ONLY):Patients with M2 marrow or better are eligible; patients with M3 or M4 marrow (greater than 25% lymphoblasts) will not be eligible to be randomized * Rating: M0, M1; Blast Cells (%): 0-5.0 * Rating: M2; Blast Cells (%): 5.1-25.0 * Rating: M3; Blast Cells (%): \> 25-50 * Rating: M4; Blast Cells (%): \> 50.0 * The term "blast cell" includes any cell that cannot be classified as a more mature normal element, and includes "leukemic cells," pathologic lymphocytes, and stem cells * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) (CONFIRMATION OF TOLERABILITY AND PHASE III ONLY): Absolute neutrophil count (ANC) \>= 750/mm\^3 * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) (CONFIRMATION OF TOLERABILITY AND PHASE III ONLY): Platelet count \>= 75,000/mm\^3 * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) (CONFIRMATION OF TOLERABILITY AND PHASE III ONLY): Total bilirubin =\< 1.5 x upper limit of normal (ULN), except for patients with known Gilbert's syndrome * RANDOMIZATION ELIGIBILITY CRITERIA (STEP 2) (CONFIRMATION OF TOLERABILITY AND PHASE III ONLY): Aspartate aminotransferase (AST) =\< 8 x upper limit of normal (ULN) EXCLUSION CRITERIA * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Patients who have BCR-ABL fusion transcript determined by fluorescence in situ hybridization (FISH) or real time-polymerase chain reaction (RT-PCR) or t(9;22)(q34;q11) by cytogenetics are not eligible and should be considered for enrollment on studies that incorporate imatinib during induction; please note: patients must also be assessed for CD20 positivity and other markers; positivity for CD22 and CD20 is defined as baseline expression of the CD22 or CD20 antigen in more than 20% of leukemic cells using local multiparameter flow-cytometric immunophenotyping with the use of CD45 expression as a marker to gate the ALL blast population, according to recommendations from the European LeukemiaNet * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): No prior therapy for ALL except for limited treatment (=\< 7 days) with corticosteroids or hydroxyurea and a single dose of intrathecal cytarabine; however, patients who are being treated with chronic steroids for other reasons (for example, to treat asthma, autoimmune disorders, lupus, etc.) are eligible * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): No prior therapy for acute leukemia except emergency therapy (corticosteroids or hydroxyurea) for blast cell crisis, superior vena cava syndrome, or renal failure due to leukemic infiltration of the kidneys; when indicated, leukapheresis or exchange transfusion is recommended to reduce the WBC * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Not pregnant and not nursing, because this study involves agents that have known genotoxic, mutagenic and teratogenic effects; therefore, for women of childbearing potential only, a negative urine or serum pregnancy test done =\< 8 days prior to registration is required * REGISTRATION ELIGIBILITY CRITERIA (STEP 1): Patients with down syndrome are excluded from this study due to the likelihood of excessive toxicity resulting; these patients should be treated in consultation with a pediatric oncologist