The use of chimeric antigen receptor (CAR)-modified T cells as a therapy for hematologic malignancies and solid tumors is becoming more widespread. However, the infusion of a T-cell product targeting a single tumor-associated antigen may lead to target antigen modulation under this selective pressure, with subsequent tumor immune escape. With the purpose of preventing this phenomenon, we have studied the impact of simultaneously targeting two distinct antigens present on tumor cells: namely mucin 1 and prostate stem cell antigen, both of which are expressed in a variety of solid tumors, including pancreatic and prostate cancer. When used individually, CAR T cells directed against either tumor antigen were able to kill target-expressing cancer cells, but tumor heterogeneity led to immune escape. As a combination therapy, we demonstrate superior antitumor effects using both CARs simultaneously, but this was nevertheless insufficient to achieve a complete response. To understand the mechanism of escape, we studied the kinetics of T-cell killing and found that the magnitude of tumor destruction depended not only on the presence of target antigens but also on the intensity of expression-a feature that could be altered by administering epigenetic modulators that upregulated target expression and enhanced CAR T-cell potency.