Quantifiers like ``all'' and ``every'' are frequent in daily language. However, when a sentence contains two quantifiers or is ``doubly-quantified'' (e.g., ``Every boy ate a cookie'') the meaning can often be ambiguous since there are two potential interpretations: collective (e.g., several boys sharing a single cookie) and distributive (e.g., several boys each eating their own cookie). Psycholinguistic studies have established empirical evidence for conflict between interpretations of a doubly-quantified sentence and have proposed that the interpretation of these sentences is ``underspecified''. However, little is known about the the neural mechanisms that support the interpretation of doubly-quantified sentences. In an fMRI experiment we demonstrate that conflict between possible interpretations of doubly-quantified sentences is supported by brain regions situated in fronto-parietal cortex. We propose that an ``underspecified'' account is insufficient to account for our neuroanatomical results and instead argue that strategic decision-making resources may support the interpretation of doubly-quantified sentences.