We present a novel conjecture concerning the scope ambiguities that arise in sentences including multiple nonreferential quantifiers. We claim that many existing theories of the phenomenon fail to correctly limit the set of readings that such sentences engender by failing to distinguish between referential and non-referential quantifiers. Once the distinction is correctly drawn, we show that surface syntax can be made, via an extended notion of surface constituency, to identify the set of available differently-scoped readings for such sentences. We examine various English constructions to show that the scopings predicted by the conjecture are the only ones that are available to human language understanders. We show how to incorporate this conjecture into a theory of quantifier scope, by couching it in a unification-based Combinatory Categorial Grammar framework and implementing it in SICStus Prolog. Finally, we compare the proposal with related approaches to quantifier scope ambiguity.