While there is wide consensus that teams are dynamic multilevel systems, little empirical research has investigated them as such and therefore our theoretical understanding is lacking. Here, we advance an integrative approach leveraging insights from team composition theories that go well beyond considering the amount or distribution of members’ individual attributes. Specifically, we focus on how the alignment of members’ multiple and simultaneous role tendencies relate to different team performance trajectories. Using a sample of 386 members of 92 teams who competed over time in a business simulation, we differentiate four different performance trajectories indicative of different developmental processes. Our findings reveal that teams composed of generalists typically exhibit moderate to strong performance throughout the two-and-a-half-month task, while teams of specialists experience a slow start due to coordination demands. Nevertheless, teams of diverse specialists can excel after they get their footing. Importantly, our study is the first to advance a theoretical and empirical model of complex systems of team member attributes as related to dynamic team performance. We conclude with directions for future research adopting more nuanced views of team composition and understanding of dynamic criterion relationships.