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The Seychelles Child Development Study (SCDS) examines the effects of prenatal exposure to methylmercury on the functioning of the central nervous system. The SCDS data include 20 outcomes measured on 9-year-old children that can be classified broadly in four outcome classes or “domains”: cognition, memory, motor, and social behavior. Previous analyses and scientific theory suggest that these outcomes may belong to more than one of these domains, rather than only a single domain as is frequently assumed for modeling. We present a framework for examining the effects of exposure and other covariates when the outcomes may each belong to more than one domain and where we also want to learn about the assignment of outcomes to domains. Each domain is defined by a sentinel outcome, which is preassigned to that domain only. All other outcomes can belong to multiple domains and are not preassigned. Our model allows exposure and covariate effects to differ across domains and across outcomes within domains, and includes random subject-specific effects that model correlations between outcomes within and across domains. We take a Bayesian MCMC approach. Results from the Seychelles study and from extensive simulations show that our model can effectively determine sparse domain assignment, and at the same time give increased power to detect overall, domain-specific, and outcome-specific exposure and covariate effects relative to separate models for each endpoint. When fit to the Seychelles data, several outcomes were classified as partly belonging to domains other than their originally assigned domains. In retrospect, the new partial domain assignments are reasonable and, as we discuss, suggest important scientific insights about the nature of the outcomes. Checks of model misspecification were improved relative to a model that assumes each outcome is in a single domain. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]