This phase II trial studies how well inotuzumab ozogamicin works in treating younger patients with B-lymphoblastic lymphoma or CD22 positive B acute lymphoblastic leukemia that has come back (relapsed) or does not respond to treatment (refractory). Inotuzumab ozogamicin is a monoclonal antibody, called inotuzumab, linked to a toxic agent called ozogamicin. Inotuzumab attaches to CD22 positive cancer cells in a targeted way and delivers ozogamicin to kill them.

This randomized phase III trial studies how well combination chemotherapy works in treating young patients with newly diagnosed B acute lymphoblastic leukemia that is likely to come back or spread, and in patients with Philadelphia chromosome (Ph)-like tyrosine kinase inhibitor (TKI) sensitive mutations. Chemotherapy drugs, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving more than one drug (combination chemotherapy) and giving the drugs in different doses and in different combinations may kill more cancer cells.