Cancer cells commonly develop resistance to immunotherapy by loss of antigen expression. Combinatorial treatments that increase levels of the target antigen on the surface of cancer cells have the potential to restore efficacy to immunotherapy. Here, we use our CRISPR interference- and CRISPR activation-based functional genomics platform to systematically identify pathways controlling cell surface expression of the multiple myeloma immunotherapy antigen B-cell maturation antigen (BCMA). We discovered that pharmacologic inhibition of HDAC7 and the Sec61 complex increased cell surface BCMA, including in primary patient cells. Pharmacologic Sec61 inhibition enhanced the antimyeloma efficacy of a BCMA-targeted antibody-drug conjugate. A CRISPR interference chimeric antigen receptor T cells (CAR-T cells) coculture screen enabled us to identify both antigen-dependent and antigen-independent mechanisms controlling response of myeloma cells to BCMA-targeted CAR-T cells. Thus, our study shows the potential of CRISPR screens to uncover mechanisms controlling response of cancer cells to immunotherapy and to suggest potential combination therapies.