Protein-protein interactions control a large range of biological processes and their identification is essential to understand the underlying biological mechanisms. To complement experimental approaches, in silico methods are available to investigate protein-protein interactions. Cross-docking methods, in particular, can be used to predict protein binding sites. However, proteins can interact with numerous partners and can present multiple binding sites on their surface, which may alter the binding site prediction quality. We evaluate the binding site predictions obtained using complete cross-docking simulations of 358 proteins with 2 different scoring schemes accounting for multiple binding sites. Despite overall good binding site prediction performances, 68 cases were still associated with very low prediction quality, presenting individual area under the specificity-sensitivity ROC curve (AUC) values below the random AUC threshold of 0.5, since cross-docking calculations can lead to the identification of alternate protein binding sites (that are different from the reference experimental sites). For the large majority of these proteins, we show that the predicted alternate binding sites correspond to interaction sites with hidden partners, that is, partners not included in the original cross-docking dataset. Among those new partners, we find proteins, but also nucleic acid molecules. Finally, for proteins with multiple binding sites on their surface, we investigated the structural determinants associated with the binding sites the most targeted by the docking partners.