In this paper I propose how to model the relation between the meaning and the syntax of lexical items in a way which allows to account for all argument alternations in any language despite the absence of an adequate and complete representation of lexical knowledge for any language. The proposed model assumes an empirical, corpus-based collection of the patterns of participant-to-function mappings for classes of verbs in a given language (such as Levin 1993 and its follow-ups for English) and represents the alternative mappings without committing the grammar writer to represent the speakers’ knowledge of the world. The proposed model cabe interfaced with a representation of lexical knowledge when one becomes available. In the interim, the present proposal together with some earlier work on the representation of argument structure (in particular, Kibort 2007, 2008, 2013) can, for the first time, be considered a complete stand-alone tool to create an inventory of constructions involving argument alternations in a language. Since the available argument structure operations are represented in the same way across languages regardless of their realisation, the model should be useful for descriptive and typological studies. It may also be a helpful step forward for computational grammars grappling with how to capture the wide range of argument alternations systematically: although it is far from representing full lexical knowledge, it is sufficient to capture the fact that some alternations are determined by semantic factors, and formally to relate the alternating variants to one another.