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The social structure of an animal population can often influence movement and inform researchers on a species' behavioral tendencies. Animal social networks can be studied through movement data; however, modern sources of data can have identification issues that result in multiply-labeled individuals. Since all available social movement models rely on unique labels, we extend an existing Bayesian hierarchical movement model in a way that makes use of a latent social network and accommodates multiply-labeled movement data (MLMD). We apply our model to drone-measured movement data from Risso's dolphins (Grampus griseus) and estimate the effects of sonar exposure on the dolphins' social structure. Our proposed framework can be applied to MLMD for various social movement applications. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]