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Thousands of human proteins function by binding short linear motifs embedded in intrinsically disordered regions that can sample different conformations. How affinity and specificity are encoded in these regions and the relative contribution of structured and dynamic binding modes is not completely understood. Here we present a complete map of specificity encoding in a PDZ domain binding to a structurally heterogeneous disordered ligand and use this map to reprogram binding to new ligands. Quantifying >200,000 energetic interactions between the PDZ domain and its ligand identifies 17 residues that control specificity for six sites in the ligand through both direct and allosteric mechanisms. Most sites where specificity can be controlled through the domain are in the structured part of the ligand, but dynamic residues additively contribute to binding affinity and communicate with structured ligand residues to enable specificity changes. Combining mutations in each of the six PDZ domain modules allows specificity to be quantitatively reprogrammed to recognize new ligands. This approach of quantifying the specificities of thousands of proteins in a single experiment should allow many different types of molecular interaction to be understood and interpretably reprogrammed.