This phase I trial studies the side effects and best dose of CS1-chimeric antigen receptor (CAR) T therapy after chemotherapy in treating patients who have CS1 positive multiple myeloma that has come back (relapsed) or does not respond to treatment (refractory). Immune cells can be engineered to kill multiple myeloma cells by inserting a piece of deoxyribonucleic acid (DNA) into the immune cells using a lentiviral vector such as CS1, that allows them to recognize multiple myeloma cells. These engineered immune cells, CS1-CAR T cells, may kill multiple myeloma cells.
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