Infusion of Allogeneic, 3rd Party CD19-specific T Cells

The goal of this clinical research study is to learn if researchers can successfully and safely give patients who have had a stem cell transplant an infusion of white blood cells (called T-cells) that have been collected from an unrelated person, and that have been genetically changed. The process of changing the DNA (genetic material) of these T-cells is called "gene transfer." The gene transfer involves drawing blood from an unrelated donor, separating out T cells using a machine, changing the cells' DNA in the laboratory, and returning the genetically changed cells back to the body. T-cells are a type of white blood cell that fight infection. The type of gene transfer being used in this study is designed to help your T-cells to better fight cancer by targeting a chemical marker that is found on certain cancer cells. Researchers want to learn if these genetically-changed T-cells can help to control B-cell leukemia or lymphoma after a stem cell transplant. Researchers want to find out the highest tolerable dose of these T-cells that can be given to patients with relapsed leukemia or lymphoma.