Although Chimeric Antigen Receptor (CAR) T-cells have shown high efficacy in hematologic malignancies, they can cause severe to life-threatening side effects. To address these safety concerns, we have developed adaptor CAR platforms, like the UniCAR system. The redirection of UniCAR T-cells to target cells relies on a Target Module (TM), containing the E5B9 epitope and a tumor-specific binding moiety. Appropriate UniCAR-T activation thus involves two interactions: between the TM and the CAR T-cell, and the TM and the target cell. Here, we investigate if and how alterations of the amino acid sequence of the E5B9 UniCAR epitope impact the interaction between TMs and the UniCAR. We identify the new epitope E5B9L, for which the monoclonal antibody 5B9 has the greatest affinity. We then integrate the E5B9L peptide in previously established TMs directed to Fibroblast Activation Protein (FAP) and assess if such changes in the UniCAR epitope of the TMs affect UniCAR T-cell potency. Binding properties of the newly generated anti-FAP-E5B9L TMs to UniCAR and their ability to redirect UniCAR T-cells were compared side-by-side with the ones of anti-FAP-E5B9 TMs. Despite a substantial variation in the affinity of the different TMs to the UniCAR, no significant differences were observed in the cytotoxic and cytokine-release profiles of the redirected T-cells. Overall, our work indicates that increasing affinity of the UniCAR to the TM does not play a crucial role in such adaptor CAR system, as it does not significantly impact the potency of the UniCAR T-cells.