Rooth (1985, 1992) analyzes focus as introducing sets of alternative meanings, which can then project by pointwise composition. This paper presents evidence that focus requires a different mechanism of alternative generation. A focused constituent introduces a set of structural alternatives, which then ‘project’ in a pointwise way in syntax, to generate sets of larger and larger linguistic expressions. A production experiment provides evidence for the need of syntactic alternative projection. The analysis builds on Potts's (2007) analysis of mixed quotation, which formalizes a grammar that can operate over expressions of the grammar. The proposal here is that certain operators, such as the focus operator ∼, operate over sets of linguistic expressions and their meanings. Syntactic projection may also explain puzzling facts in other domains, such as echo questions and disjunction.