In this chapter, we will offer a new way of analysing the syntax and semantics of the mass/count distinction at the syntax-semantics interface, by synthesising the constructionist framework originating in Borer (2005) with the (lexicalist) `iceberg semantics' proposed in Landman (2011, 2016. We believe that this synthesis has several conceptual and empirical advantages over existing frameworks. It combines the flexibility and morphosyntax-driven nature of constructivism with an explicit role for human conceptual categories such as INDIVIDUAL and SUBSTANCE. It allows us to distinguish between different kinds of mass/count shifts and makes explicit why some of them are harder than others. Furthermore, it clarifies the distinction between stuff-reference, number neutrality and non-countability, three distinct (although interdependent) nominal properties that are often explicitly or implicitly conflated in existing accounts of the mass/count distinction.