The “turn-taking” system, a notion referring to the dynamics of verbal exchanges in face-to-face interaction, is often presented as the hallmark of human language (Levinson, 2016). However, recent works have investigated turn-taking mechanisms in several nonhuman taxa, thus referring to the moment-by-moment coordinated alternation of actions or vocalizations, for instance in primates or birds. These findings have been interpreted as evidence of elementary forms of sequence organization in the animal world, and therefore as evidences of an evolutionary pathway, leading from very rough forms of signal alternation, to the complex multimodal and conversational turn-taking system used by humans. This article first reviews and discusses these findings. It then makes the case for going beyond the study of uniquely intra-specific forms of communication and interaction. It argues that considering interspecies interaction is of interest for social sciences in general, and linguistics scholarship in particular, at least in two respects. First, on an empirical level, to investigate a widespread phenomenon, namely ordinary human-animal interactions, as it occurs mostly in domestic settings—a topic that has been relatively neglected in the study of social interaction so far (for a range of reasons that we shall touch on). Secondly, on a more speculative level, it assumes that ordinary interspecies interactions, especially as they unfold with domestic pets or wild animals in natural settings (vs. in experimental settings), are a valuable locus to explore rudimentary forms of sequence organization, that are neither governed by linguistic and cultural norms, nor entirely the product of stereotypical species-related behavioral patterns. We posit that fundamental principles of sociality are to be found in the contextual adjustments of multimodal actions and in the emergence of meaning in interspecies interactions.