Dialectical fallacies are typically defined as breaches of the rules of a regulated discussion between two participants (di-logue). What if discussions become more complex and involve multiple parties with distinct positions to argue for (poly-logues)? Are there distinct argumentation norms of polylogues? If so, can their violations be conceptualized as polylogical fallacies? I will argue for such an approach and analyze two candidates for argumentative breaches of multi-party rationality: false dilemma and collateral straw man.