Refractory Adult Acute Lymphoblastic Leukemia

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 I trial studies the side effects and best dose of CD4+ and CD8+ HA-1 T cell receptor (TCR) (HA-1 T TCR) T cells in treating patients with acute leukemia that persists, has come back (recurrent) or does not respond to treatment (refractory) following donor stem cell transplant. T cell receptor is a special protein on T cells that helps them recognize proteins on other cells including leukemia. HA-1 is a protein that is present on the surface of some peoples' blood cells, including leukemia. HA-1 T cell immunotherapy enables genes to be added to the donor cells to make them recognize HA-1 markers on leukemia cells.