Refractory Chronic Myeloid Leukemia Bcr Abl1 Positive

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.

This phase I trial tests the safety, side effects and best dose of anti-CD19/20/22 chimeric antigen receptor (CAR) T cells (TriCAR19.20.22 T cells) and how well they work in treating patients with non-Hodgkin lymphoma, acute lymphoblastic leukemia (ALL) and chronic lymphocytic leukemia (CLL) that has come back after a period of improvement (relapsed) or that has not responded to previous treatment (refractory). CAR T-cell therapy is a type of treatment in which a patient's T cells (a type of immune system cell) are changed in the laboratory so they will attack cancer cells. T cells are taken from a patient's blood. Then the gene for a special receptor that binds to a certain protein, such as CD19, CD20 and CD22, on the patient's cancer cells is added to the T cells in the laboratory. The special receptor is called a CAR. Large numbers of the CAR T cells are grown in the laboratory and given to the patient by infusion for treatment of certain cancers. Giving TriCAR19.20.22 T cells may be safe, tolerable, and/or effective in treating patients with relapsed or refractory non-Hodgkin lymphoma, ALL and CLL.