BLOCK I: Patients receive dexamethasone orally (PO) or intravenously (IV) thrice daily (TID) on days 1-8 and 21-28; vincristine sulfate IV on days 1, 21, 28, and 35; rituximab IV on days 4, 13, 20, and 27; clofarabine, cyclophosphamide, and etoposide IV on days 6-10; aldesleukin subcutaneously (SC) once every other day (QOD) on days 11-19; and pegaspargase IV on days 21, 28, and 35. Patients also undergo natural killer (NK) cell infusion on day 12. Patients may receive triple intrathecal therapy comprising methotrexate, therapeutic hydrocortisone, and cytarabine on days 1, 5, 8, 11, 21, and 28. Patients continue on to Block II after count recovery.