Tackling grand challenges requires coordination and sustained effort among multiple organizations and stakeholders. Yet research on stakeholder theory has been conceptually constrained in capturing this complexity: existing accounts tend to focus either on dyadic level firm-stakeholder ties, or on stakeholder networks within which the focal organization is embedded. We suggest that addressing grand challenges requires a more generative conceptualization of organizations and their constituents as stakeholder systems. Using the metaphor of ballet and insights from Dance Theory, we highlight four defining dimensions of stakeholder systems (two structural and two dyadic); we proceed to offer a dynamic model of how those dimensions may interact and co-evolve. Our metaphor and resulting theory of stakeholder systems are thereby well-equipped to incorporate the complexity of tackling grand challenges, where many contemporary stakeholder arrangements are oriented around issues rather than firms.