Researchers seeking to analyse how intersubjectivity is established and maintained face significant challenges. The purpose of this article is to provide theoretical/methodological tools that begin to address these challenges. I develop these tools by applying several concepts from multimodal (inter)action analysis to an excerpt taken from the beginning of a tutoring session, drawn from a wider data set of nine one-to-one tutoring sessions. Focusing on co-produced higher-level actions as an analytic site of intersubjectivity, I show that lower-level actions that co-constitute a higher-level action can be delineated into tiers of materiality. I identify three tiers of materiality: durable, adjustable and fleeting. I introduce the theoretical/methodological tool tiers of material intersubjectivity to delineate these tiers analytically from empirical data, and show how these tiers identify a multimodal basis of material intersubjectivity. Building on this analysis I argue that the durable and adjustable tiers of material intersubjectivity produce the interactive substrate, which must be established in order for actions that display fleeting materiality to produce intersubjectivity. These theoretical/methodological tools extend the framework of multimodal (inter)action analysis, and I consider some potential applications beyond the example used here.