Chimeric antigen receptor (CAR) gene-modified T cells (CAR T cells) can eradicate B cell malignancies via recognition of surface-expressed B lineage antigens. Antigen escape remains a major mechanism of relapse and is a key barrier for expanding the use of CAR T cells towards solid cancers with their more diverse surface antigen repertoires. In this review we discuss strategies by which cancers become amenable to effective CAR T cell therapy despite heterogeneous phenotypes. Pharmaceutical approaches have been reported that selectively upregulate individual target antigens on the cancer cell surface to sensitize antigen-negative subclones for recognition by CARs. In addition, advanced T cell engineering strategies now enable CAR T cells to interact with more than a single antigen simultaneously. Still, the choice of adequate targets reliably and selectively expressed on the cell surface of tumor cells but not normal cells, ideally by driving tumor growth, is limited, and even dual or triple antigen targeting is unlikely to cure most solid tumors. Innovative receptor designs and combination strategies now aim to recruit bystander cells and alternative cytolytic mechanisms that broaden the activity of CAR-engineered T cells beyond CAR antigen-dependent tumor cell recognition.