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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 targets of inference. We use a Bayesian approach to RLCMs in order to use informative prior assumptions on the number and definitions of latent classes to be consistent with scientific knowledge so that the posterior distribution tends to concentrate on smaller numbers of clusters and sparser binary patterns. The paper derives a posterior sampling algorithm based on Markov chain Monte Carlo with split‐merge updates to efficiently explore the space of clustering allocations. Through simulations under the assumed model and realistic deviations from it, we demonstrate greater interpretability of results and superior finite‐sample clustering performance for our method compared to common alternatives. The methods are illustrated with an analysis of protein data to detect clusters representing autoantibody classes among scleroderma patients. [ABSTRACT FROM AUTHOR]