The purpose of this study is to assess the impact of adding blood stem cells to CAR T-cell therapy in an effort to improve cancer treatment. CAR T-cell therapy is a type of treatment in which a patient's T-cells (a type of immune cell) are changed in the laboratory so that they attack cancer cells. T-cells are taken from a patient’s blood, and 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 CAR T-cells are grown in the laboratory and given to the patient by infusion. CAR T-cell therapy requires chemotherapy prior to treatment. Participants in this study are patients who are eligible to receive one of the current CAR T-cell therapies approved by the U.S. Food and Drug Administration (FDA) for relapsed or refractory B-cell acute lymphoblastic leukemia, non-Hodgkin lymphoma, or multiple myeloma. The FDA has approved CAR T-cell therapy for the treatment of certain cancers, but its use in this study is considered to be investigational. During this study, more CAR T-cell therapies may become FDA-approved and available for use.