Language is fundamental to the human ability to work collaboratively on shared tasks. Current theories of dialogue, the format in which language use is shared and coordinated, emphasize cognitive processes that bring conversational partners’ talk into alignment. Driven by automatic priming of linguistic representation and the synchronization of embodied actions, the success of an interacting pair is ascribed to the degree to which the two converge. Such convergence, however, cannot explain how language use allows dyads to extend their abilities beyond those at the individual level, nor how a dyad might produce a novel idea. Instead, a new theory of dialogue must be developed, one that takes into account both convergent processes as well as processes that support divergence and complementarity. Borrowing a theoretical framing from dynamical systems and extended cognition, such a model is described as an interpersonal synergy. The role of divergence in supporting collaboration is tested across three domains in which collaboration has been previously tested. In Experiment 1, we test whether linguistic divergence supports joint decision making in a perceptual task, replicating and extending previous work that found that indiscriminate alignment negatively correlates with collective benefit. In Experiment 2, dyads engage in a creative humor production task together and alone. Here we correlate turn-by-turn divergence with collaborative success. In Experiment 3 we explore the extent to which overlapping or complementary contributions assist in the construction of a collaborative memory over repeated conversational rehearsals. Across these three domains different methods for measuring conversational divergence are established. We find that turn-by-turn progressivity predicts the extent to which pairs produce more humorous and creative jokes. However, we fail to correlate measures of conversational divergence with collaborative benefit in the decision-making and memory tasks. These studies and new methods represent a first step in developing a fuller theory of dialogue as the basis for the coordination of distinct information and contributions, such that both convergent and divergent processes may benefit the ability of conversational partners to engage in socially extended cognitive activities.