Verb multi-word expressions (VMEs) constitute a general feature of natural languages; many empirical studies have documented their widespread use in both oral and written communication. However, their mastery as an integral part of communicative competence is challenging for learners of a second/foreign language (L2). Given that the relevant literature focuses almost exclusively on the examination of their semantic properties, the purpose of this research is to study VMEs’ syntactic behavior and categorize them in a way that can help the teaching of Modern Greek as a L2. To this effect, we adapted a model of VME morphosyntactic description to first analyze the set of VMEs of the especially productive MG verb κάνω (to do). Since κάνω is considered an auxiliary verb, we further conducted an analysis of other MG verbs with similar syntactic structure in order to elucidate whether its behavior is generalizable or idiosyncratic. Using as a main criterion the degree of VME syntactic consolidation, the tripartite distinction into fixed, semi-fixed and syntactically flexible expressions proposed in the literature was confirmed. The range of their specific morphosyntactic transformations was investigated through available MG text corpora. More importantly, our results show that the vast majority of the structures under consideration are syntactically flexible. At a theoretical level, this implies that the stability of these structures is more relative than generally thought, while, at a more practical one, it underscores the need for further research on the categories that need overt teaching.