Antigen escape can compromise the efficacy of chimeric antigen receptor (CAR-) or T cell receptor (TCR-) engineered T cells. Targeting multiple antigens can effectively limit antigen escape, and combining CAR- with TCR-mediated targeting can significantly broaden the spectrum of targetable antigens. Here, we explored whether dual-antigen specificity can be installed on T cells using combined TCR- and CAR-engineering to prevent antigen escape of multiple myeloma (MM). We report the generation of CD8 T cells that were transduced to express a transgenic TCR, targeting a peptide derived from transcriptional coactivator BOB1 in the context of HLA-B*07:02, alongside a BCMA-targeting CAR. Those T cells, termed TRaCR T cells, efficiently recognized target cells that were resistant to either BOB1 TCR or BCMA CAR T cells, illustrating general dual-specificity. In the presence of both antigens however, target cell recognition was preferentially conferred via the CAR, compromising TCR-mediated target cell recognition. Importantly, this resulted in a survival advantage for tumor cells lacking expression of BCMA in an in vivo model of heterogenous MM. In conclusion, we demonstrate general dual-specificity of TRaCR T cells but advise caution when using TRaCR T cells as strategy to target heterogenous tumors.