Many important cellular protein interactions are mediated by peptide recognition domains. The ability to predict a domain's binding specificity directly from its primary sequence is essential to understanding the complexity of protein-protein interaction networks. One such recognition domain is the PDZ domain, functioning in scaffold proteins that facilitate formation of signaling networks. Predicting the PDZ domain's binding specificity was a part of the DREAM4 Peptide Recognition Domain challenge, the goal of which was to describe, as position weight matrices, the specificity profiles of five multi-mutant ERBB2IP-1 domains. We developed a method that derives multi-mutant binding preferences by generalizing the effects of single point mutations on the wild type domain's binding specificities. Our approach, trained on publicly available ERBB2IP-1 single-mutant phage display data, combined linear regression-based prediction for ligand positions whose specificity is determined by few PDZ positions, and single-mutant position weight matrix averaging for all other ligand columns. The success of our method as the winning entry of the DREAM4 competition, as well as its superior performance over a general PDZ-ligand binding model, demonstrates the advantages of training a model on a well-selected domain-specific data set.