In interorganizational teams, processes are more complex and structures less clear than in intraorganizational settings. Different perspectives come together and authoritative positions are often ambiguous, which makes establishing what to do problematic. We adopt a ventriloquial analytical lens and pose the question: How exactly do interorganizational team members build a collaborative strategy under these conditions, in their situated interactions? Our findings show how many different voices (individual, organizational, team, and other) shape members’ strategy-making and reveal these voices’ performative authoritative effects: Members established their team’s strategy and produced the needed authority to do so through three coauthoring practices, namely, the proposition, appropriation, and expropriation of voices. When members switched between the practices and different voices, these voices were either woven together or moved apart. We sketch a conceptualization of strategy as a relational assemblage and develop a process model of strategy-coauthoring to illuminate these dynamics.