MC-10029

This phase I trial tests safety, side effects and best dose of B-cell activating factor receptor (BAFFR)-based chimeric antigen receptor T-cells, with fludarabine and cyclophosphamide lymphodepletion, for the treatment of patients with B-cell hematologic malignancies that has come back after a period of improvement (relapsed) or that does not respond to treatment (refractory). BAFFR-based chimeric antigen receptor T-cells 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 on the patient's cancer cells is added to the T cells in the laboratory. The special receptor is called a chimeric antigen receptor (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 chemotherapy, such as fludarabine and cyclophosphamide, helps ill cancer cells in the body and helps prepare the body to receive the BAFFR based chimeric antigen receptor T-cells. Giving BAFFR based chimeric antigen receptor T-cells with fludarabine and cyclophosphamide for lymphodepletion may work better for the treatment of patients with relapsed or refractory B-cell hematologic malignancies.