The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM to an arbitrary number of variables and show how the parameters of this multivariate model can be estimated using a maximum likelihood or a restricted maximum likelihood approach. Overall, the two likelihood approaches provide consistent and efficient parameter estimates and can be used to investigate a multitude of interesting research questions.