It is generally assumed that the weak crossover (WCO) effect arises when an operator fails to bind a pronoun that stands in a particular syntactic configuration with the given operator. In this article, I introduce a new kind of crossover effect in which the binding dependencies of two different operators work in tandem to yield the given effect. The new effect is radically different from the traditional crossover cases, which involve the binding dependency of just one operator. I show that theories that define the WCO principle as a condition regulating the binding of pronouns cannot account for the new effect. I also show that to account for all the varieties of crossover effects, the WCO principle must be defined as a condition regulating the semantic relation of dependence and must make use of the notion of Spell-Out domain discussed by Chomsky (2001, 2004).