The goal of this article is to investigate the factors that affect the acceptability and processing of they. Previous research has sought to determine whether there are acceptability and processing differences between they/themselves with plural vs. singular antecedents, with mixed results. The studies reported here address this question using bound variable singular they (e.g., Every customer claimed that they were first in line). We asked whether bound singular they is sensitive to both the morphological number and the semantic distributivity of the binding quantifier phrase. We contrasted morphologically singular quantified antecedents (every and each) with plural quantified antecedents (all). Instead of finding an effect of number, we found an effect of semantic distributivity in acceptability, with bound singular they demonstrating a cline of preference toward more distributive antecedents. Neither number nor distributivity, however, registered as an effect on reading times. Rather, for all types of quantified antecedents, encountering a pronoun like he or she rather than they registered a processing delay, in contrast to non-quantified antecedents. Our results are most fully compatible with the view that they is underspecified for number properties.