T cells must respond differently to antigens of varying affinity presented at different doses. Previous attempts to map peptide MHC (pMHC) affinity onto T-cell responses have produced inconsistent patterns of responses, preventing formulations of canonical models of T-cell signaling. Here, a systematic analysis of T-cell responses to 1 million-fold variations in both pMHC affinity and dose produced bell-shaped dose-response curves and different optimal pMHC affinities at different pMHC doses. Using sequential model rejection/identification algorithms, we identified a unique, minimal model of cellular signaling incorporating kinetic proofreading with limited signaling coupled to an incoherent feed-forward loop (KPL-IFF) that reproduces these observations. We show that the KPL-IFF model correctly predicts the T-cell response to antigen copresentation. Our work offers a general approach for studying cellular signaling that does not require full details of biochemical pathways.