In signaling networks, many protein-protein interactions are mediated by modular domains that bind short linear motifs. The motifs' sequences modulate many factors, among them affinity and specificity, or the ability to bind strongly and to bind the appropriate partners. Previous studies have proposed a trade-off between affinity and specificity, suggesting that motifs with high affinity are less capable of differentiating between domains with similar sequences and structures. Using Deep Mutational Scanning to create a mutant library of a well characterized binding motif, and protein complementation assays to measure protein-protein interactions, we tested this trade-offin vivofor the first time. We measured the binding strength and specificity of a library of mutants of a binding motif on the MAP kinase kinase Pbs2, which binds the SH3 domain of the osmosensor protein Sho1 inSaccharomyces cerevisiae. We find that many mutations in the region surrounding the binding motif modulate binding strength, but that few mutations have a strong impact on specificity. Moreover, we find no systematic relationship between affinity and specificity as measuredin vivo. Interestingly, all Pbs2 mutations which increase affinity or specificity are situated outside of the Pbs2 residues that interact with the canonical SH3-binding pocket, suggesting that other surfaces on Sho1 contribute to binding. We use predicted structures to propose a model of binding which involves residues neighboring the core Pbs2 motif binding outside of the canonical SH3-binding pocket, allowing affinity and specificity to be determined by a broader range of sequences than what has previously been considered.