In this paper, I examine some of the presuppositions that underpin the practice and interpretation of multi-person dialogue -- that is, in contexts involving more than two interlocutors -- with particular thought for the university seminar. I outline the 'dialogical phenomenology' of Beata Stawarska as useful on this count; however, I argue that Stawarska's account is steeped in a philosophical 'dyadic paradigm' which has limiting consequences for practitioners of dialogue looking to understand the nature of dialogue in a group context. Against this paradigm, I argue that there are many varieties of intersubjectivity that have not been widely discussed, including we-you, we-yous, I-yous and we-they intersubjective structures. I will look further at how an understanding of these structures is valuable for dialogue within educational praxes and for the Humanities more broadly.