At the intersection of corpus, cognitive linguistics and interlanguage (IL), this work models the IL properties of written constructions with may , can , must and will in four varieties of learner English (Chinese-, French-, German- and Swedish-English interlanguage) and British English. Following the usage-based assumption that linguistic knowledge is both item-specific and schematic in nature and based on recent psycholinguistic work showing learners' difficulties to produce native-like constructions (Ellis and Sagarra 2011), this study proposes a multifactorial way of exploring learners' knowledge of constructions at concrete and schematic levels, simultaneously. Specifically, 1903 constructions are investigated using a comprehensive corpus annotation scheme and multinomial regression modelling. This work reveals different patterns of central tendency of constructions across IL and native English. Crucially, it emerges that although, abstractly, learners and native speakers share similar schematic constructs, more superficially, learners' linguistic representations of those constructs systematically deviate from those of natives. Ultimately, this work sets the scene for experimental research on prototypical non-native modal constructions and raises the question of what constitutes an adequate level of (corpus) description for the profiling of IL grammars.