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This paper presents a model-based method for clustering multivariate binary observations that incorporates constraints consistent with the scientific context. The approach is motivated by the precision medicine problem of identifying autoimmune disease patient subsets or classes who may require different treatments. We start with a family of restricted latent class models or RLCMs. However, in the motivating example and many others like it, the unknown number of classes and the definition of classes using binary states are among the tar