Correlations between anomalous activity patterns can yield pertinent information about complex social processes: a significant deviation from normal behavior, exhibited simultaneously by multiple pairs of actors, provides evidence for some underlying relationship involving those pairs---i.e., a multilateral relation. We introduce a new nonparametric Bayesian latent variable model that explicitly captures correlations between anomalous interaction counts and uses these shared deviations from normal activity patterns to identify and characterize multilateral relations. We showcase our model's capabilities using the newly curated Global Database of Events, Location, and Tone, a dataset that has seen considerable interest in the social sciences and the popular press, but which has is largely unexplored by the machine learning community. We provide a detailed analysis of the latent structure inferred by our model and show that the multilateral relations correspond to major international events and long-term international relationships. These findings lead us to recommend our model for any data-driven analysis of interaction networks where dynamic interactions over the edges provide evidence for latent social structure.