As immune sentinel cells, macrophages are required to respond specifically to diverse immune threats and initiate appropriate immune responses. This stimulus-response specificity (SRS) is in part encoded in the signaling dynamics of the NF{kappa}B transcription factor. While experimental stimulus-response studies have typically focused on single defined ligands, in physiological contexts cells are generally exposed to mixtures of ligands. It remains unclear how macrophages process exposure to ligand mixtures and particularly whether they are able to maintain SRS in such complex exposure conditions. Here, we leveraged an established mathematical model that captures the heterogeneous single-cell NF{kappa}B responses of macrophage populations to extend experimental studies with systematic simulations of complex mixtures containing up to five ligands. Live-cell microscopy experiments for a subset of the conditions validated model predictions but revealed a discrepancy when TLR3 and TLR9 are stimulated. Refining the model suggested that the observed but unexpected ligand antagonism arises from a limited capacity for endosomal transport which is required for response to both CpG and pIC. With the updated model, we systematically analyzed SRS across all combinatorial-ligand conditions and employed three ways of quantifying SRS involving trajectory decomposition into informative trajectory features or machine learning. Our findings show that macrophages most effectively distinguish single-ligand stimuli, and distinguishability declines as more ligands are combined. However, even in complex combinatorial conditions, macrophages still maintain a level of distinguishability that is statistically significant. These results indicate a robustness of innate immune response specificity: even in the context of complex exposure conditions, the NF{kappa}B temporal signaling code of macrophages can still classify immune threats to direct an appropriate response.