During communicative interactions, language production and comprehension are bounded by the accumulation of a shared communicative context. Besides lexical pacts and simplification of referential expressions, the creation of a shared context allows for the intelligible use of linguistic signals with novel, interaction-specific meanings. Here, we explore whether context-specific language use leads to mutual adjustment of interlocutors’ conceptual representations. We tasked dyads with solving a referential communication game, quantifying dialogue-related adjustments in interlocutors’ conceptual structures, and coordination dynamics during the interaction. After engaging in the dialogue, interlocutors judged the same set of referents more similarly than other participants engaged in the same task, but not with each other (pseudo-pairs). Exploratory analyses of the structural complexity of unfolding semantic spaces indicate a stronger alignment between interacting dyads than pseudo-pairs. These findings suggest that human communication is supported by structural coordination of conceptual representations of the communicative referents, over and above signal-level alignment.