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While the vast majority of clustering algorithms are partitional, many real world datasets have inherently overlapping clusters. Several approaches to finding overlapping clusters have come from work on analysis of biological datasets. In this paper, we interpret an overlapping clustering model proposed by Segal et al. [23] as a generalization of Gaussian mixture models, and we extend it to an overlapping clustering model based on mixtures of any regular exponential family distribution and the corresponding Bregman divergence. We provide the necessary algorithm modifications for this extension, and present results on synthetic data as well as subsets of 20-Newsgroups and EachMovie datasets.