Recurrent 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.