Humans routinely form groups to achieve goals that no individual can accomplish alone. Group coordination often brings to mind synchrony and alignment, where all individuals do the same thing (e.g., driving on the right side of the road, marching in lockstep, or playing musical instruments on a regular beat). Yet, effective coordination also typically involves differentiation, where specialized roles emerge for different members (e.g., prep stations in a kitchen or positions on an athletic team). Role specialization poses a challenge for computational models of group coordination, which have largely focused on achieving synchrony. Here, we present the CARMI framework, which characterizes role specialization processes in terms of five core features that we hope will help guide future model development: Communication, Adaptation to feedback, Repulsion, Multi-level planning, and Intention modeling. Although there are many paths to role formation, we suggest that roles emerge when each agent in a group dynamically allocates their behavior toward a shared goal to complement what they expect others to do. In other words, coordination concerns beliefs (who will do what) rather than simple actions. We describe three related experimental paradigms-"Group Binary Search," "Battles of the Exes," and "Find the Unicorn"-that we have used to study differentiation processes in the lab, each emphasizing different aspects of the CARMI framework.