This paper reconsiders the nature of floating quantifiers (FQ) in English and proposes a strictly compositional semantic approach to their distribution. The new approach builds on Fitzpatrick's (2006) sketch of a "crossing" analysis, under which the semantic composition of an FQ is made possible by moving a co-indexed DP over the FQ. This idea is formally implemented by making a minor revision to Heim and Kratzer's (1998) Predicate Abstraction, and the revision allows the rule to apply to whatever nodes exist within the path of syntactic movement. It is shown that the crossing analysis developed in this paper overcomes some empirical challenges to the stranding analysis (Sportiche 1988; Bošković 2004) and the modifier analysis (Bobaljik 1995; Brisson 1998).