This chapter draws on independent work on the syntax–semantics interface to motivate a more complex clausal architecture for an assignment-variable-based theory. Binding across syntactic categories and semantic domains is captured uniformly from a generalized binder-index feature, which attaches directly to expressions undergoing movement for type reasons. World-binding (intensionality) arises from the complementizer, which moves from the world-argument position of the clause’s main predicate; assignment-binding arises from modal elements, which move from an internal assignment-argument position of the complementizer. The semantics is fully compositional. The remainder of the book develops the account and applies it to a range of constructions and types of linguistic shifting phenomena.