A substantial part of people’s social lives unfolds within groups. Yet, there is a notable research gap concerning if and how the personality characteristics that people bring to group interactions combine to predict person and group outcomes. In this study, we used the Group-Actor-Partner-Interdependence Model (Kenny & Garcia, 2012) as a framework to integrate prior approaches and understand how the composition of two socially relevant personality traits - agency and communion — affects people and groups. We analyzed data from 432 participants (M age = 26.61, 51% female) who formed 108 four-person groups and engaged in four different group tasks. Our findings yield three key insights: (1) At the person level, people’s own trait levels were the main drivers of their behaviors, experiences, and performance. (2) At the group level, personality composition affected different outcomes compared to the person level, with agency playing an overall more important role for group behaviors and experiences. (3) Notable composition effects at both levels emerged for conflict behavior: People who were similar to their group in terms of agency were more engaged in conflicts, and groups whose members had similar agency levels were more likely to experience conflicts as a whole. We contextualize our findings within a theoretical framework to better understand when and how personality composition in social interactions is important, and we review methodologies to capture its multifaceted components.