Our multidimensional identities determine how we interact with each other, shaping social networks through group-based connection preferences. While interactions along single dimensions have been extensively studied, the dynamics driving multidimensional connection preferences remain largely unexplored. In this work, we develop a network model of multidimensional social interactions to tackle two crucial questions: What is the structure of our latent connection preferences, and how do we integrate information from our multidimensional identities to connect with others? To answer these questions, we systematically model different latent preference structures and preference aggregation mechanisms. Then, we compare them using Bayesian model selection by fitting empirical data from high school friendship networks. We find that a simple latent preference model consistently outperforms more complex alternatives. The calibrated model provides robust measures of latent connection preferences in real-world networks, bringing insights into how one- and multidimensional groups interact. Finally, we develop natural operationalizations of dimension salience, revealing which aspects of identity are most relevant for individuals when forming connections.