Accelerated Phase Chronic Myelogenous Leukemia, BCR-ABL1 Positive

This phase II clinical trial studies how well personalized natural killer (NK) cell therapy works after chemotherapy and umbilical cord blood transplant in treating patients with myelodysplastic syndrome, leukemia, lymphoma or multiple myeloma. This clinical trial will test cord blood (CB) selection for human leukocyte antigen (HLA)-C1/x recipients based on HLA-killer-cell immunoglobulin-like receptor (KIR) typing, and adoptive therapy with CB-derived NK cells for HLA-C2/C2 patients. Natural killer cells may kill tumor cells that remain in the body after chemotherapy treatment and lessen the risk of graft versus host disease after cord blood transplant.

This phase II trial studies how well blinatumomab, methotrexate, cytarabine, and ponatinib work in treating patients with Philadelphia chromosome (Ph)-positive, or BCR-ABL positive, or acute lymphoblastic leukemia that has come back or does not respond to treatment. Immunotherapy with monoclonal antibodies, such as blinatumomab, may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Drugs used in chemotherapy, such as methotrexate and cytarabine, 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. Ponatinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving blinatumomab, methotrexate, cytarabine, and ponatinib may work better in treating patients with acute lymphoblastic leukemia.