We evaluate brain structure sensitivity to verbal interference in a sentence interpretation task, building on previously reported evidence that those with better control of verbal interference show higher grey matter density in the posterior paravermis of the right cerebellum. We compare brain structure sensitivity to verbal interference control across two groups, English monolingual (N = 41) and multilingual (N = 46) adults. Using voxel-based morphometry, our primary goal was to identify and explore differences in regional patterns of grey matter sensitivity to performance on the sentence interpretation task, controlling for group variability in age, nonverbal reasoning and vocabulary knowledge. There was no group difference in performance but there was a significant group effect in grey matter sensitivity to task performance in our region of interest: stronger sensitivity in the paravermis in bilinguals compared to monolinguals in accuracy performance in the high (relative to low) verbal interference condition. This effect was observed when the linguistic interference was presented in an unfamiliar language (Greek) but not when presented in the familiar language (English). Our findings suggest that multilanguage acquisition mediates regional involvement within the language network, conferring enhanced functional plasticity within structures (including the paravermis) in the service of control of linguistic interference.