This paper examines how organizations collaborate with multiple partners, such as when they develop innovative and complex product platforms like smartphones, servers, and MRI machines that rely on technologies developed by organizations in three or more sectors. Research on multipartner alliances often treats them as a collection of independent dyads, neglecting the possibility of third-party influence and interference in dyads that can inhibit innovation. Using a multiple-case, inductive study of six groups, each composed of three organizations engaged in technology and product development in the computer industry, I examine the collaborative forms and processes that organizations use to innovate with multiple partners in groups. Groups that used the collaborative forms of independent parallel dyads or single unified triads generated mistrust and conflict that stemmed from expectations about third-party participation and overlapping roles and thus had low innovation performance and weaker ties. Other groups avoided these problems by using a dynamic collaboration process that I call "group cycling," in which managers viewed their triad as a small group, decomposed innovative activities into a series of interlinked dyads between different pairs of partners, and managed third-party interests across time. By temporarily restricting participation to pairs, managers chose which ideas, technologies, and resources to incorporate from third parties into single dyads and ensured that the outputs of multiple dyads were combined into a broader innovative whole.