Abstract: Many grammatical phenomena have been analyzed based on the assumption that constituents can introduce semantic alternatives, and that these alternatives can project in a pointwise fashion, following Hamblin’s 1973 analysis of questions. Katzir (2007) argued that at least sometimes, alternatives are structural. This presentation provides new arguments compatible with this view, which suggest that expressions can introduce syntactic alternatives, that these alternatives can “project” in a pointwise fashion, and that grammar can operate over sets of linguistic expressions. The evidence, some of which from online experiments, comes from data involving disjunction, coordination, and focus. If true, this raises interesting questions about the architecture of grammar.