We report on the first, still on-going effort to integrate verb MWEs in an LFG grammar of Modern Greek (MG). Text is lemmatized and tagged with the ILSP FBT Tagger and is fed to a MWE filter that marks Words_With_Spaces in MWEs. The output is then formatted to feed an LFG/XLE grammar that has been developed independently. So far we have identified and classified about 2500 MWEs, and have processed 40% of them by manipulating only the lexicon and not the rules of the grammar.Research on MG MWEs (indicatively, Anastasiadi-Simeonidi, 1986; Fotopoulou, 1993;Mini et al., 2011) has developed collections of MWEs and discussed classification, syntax and semantics issues. To the best of our knowledge, this is the first attempt to obtain deep parses of a wide range of types of MG verb MWEs with rich syntactic structure.