CONSOLIDATION THERAPY: Beginning after the second course of blinatumomab (patients randomized to the blinatumomab group) or after intensification therapy (patients not randomized to blinatumomab), patients receive cytarabine IV over 30 minutes or SC on days 1-5, etoposide IV over 1 hour on days 1-5, methotrexate IT on day 1, and pegaspargase IM or IV on day 5, and CD20 positive patients may optionally receive rituximab IV on day 5. Beginning 4 weeks from day 1 of course 1, patients receive cytarabine, etoposide, methotrexate, and CD20 positive patients may receive rituximab as in course 1. Beginning 4 weeks from day 1 of course 2, patients receive daunorubicin hydrochloride IV over 10-15 minutes on day 1, 8, 15, and 22; vincristine sulfate IV on days 1, 8, 15, and 22; dexamethasone PO daily on days 1-7 (and 15-21 for patients age < 55 years); methotrexate IT on day 2; cyclophosphamide PO or IV over 30 minutes on day 29; cytarabine IV over 30 minutes or SC on days 30-33 and 37-40; mercaptopurine PO on days 29-42 and CD20 positive patients may receive rituximab on day 8. Beginning 8 weeks from day 1 of course 3, patients receive cytarabine, etoposide, methotrexate, and CD20 positive patients may optionally receive rituximab as in course 1. Patients randomized to blinatumomab repeat course 4 and then receive blinatumomab IV continuously on days 1-28.