Multiword expressions (MWEs) are challenging and pervasive phenomena whose idiosyncratic properties show notably at the levels of lexicon, morphology, and syntax. Thus, they should best be annotated jointly with morphosyntax. We discuss two multilingual initiatives, Universal Dependencies and PARSEME, addressing these annotation layers in cross-lingually unified ways. We compare the annotation principles of these initiatives with respect to MWEs, and we put forward a roadmap towards their gradual unification. The expected outcomes are more consistent treebanking and higher universality in modeling idiosyncrasy.