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Merging datafiles containing information on overlapping sets of entities is a challenging task in the absence of unique identifiers, and is further complicated when some entities are duplicated in the datafiles. Most approaches to this problem have focused on the settings of record linkage, referring to linking two files assumed to be free of duplicates, or duplicate detection, referring to detecting which records in a single file are duplicates. However, it’s common in practice to encounter files that fit somewhere in between or beyond these two settings. In this article we propose a new Bayesian approach for this general setting of multifile record linkage and duplicate detection. We extend previous models for comparison data to accommodate the multifile setting and use a novel partition parameterization to propose a structured prior for partitions that can incorporate prior information about the data collection processes of the files in a flexible manner. We then propose a family of loss functions which we use to derive Bayes estimates of partitions that allow uncertain portions of the partitions to be left unresolved. The usage of our proposed methodology is illustrated through the linkage of three Colombian homicide record systems.