Transcategorial morphemes share the common ability to be used synchronically across different syntactic categories (synchronic grammaticalization). This paper first shows that transcategoriality is a general property of linguistic systems, variously exploited by languages, then addresses the theoretical questions raised by these morphemes. A new model accounting for this transcategorial functioning, named “fractal grammar”, is proposed and illustrated by various examples. The analysis for this particular functioning relates the polysemy of these morphemes to their syntactic flexibility in a dynamic way: the variation of the syntactic scope of the morpheme (“fractal functioning”) is triggered by its environment and produces its polysemy (variation of the semantic scope). Fractal grammar is thus defined by two basic mechanisms: the construal of a common image-schema (“scale invariance”), accounting for the unity of the morpheme, and the activation of “scale (or level) properties”, accounting for the semantic and syntactic variations. A typological sketch of transcategoriality is then sketched, in relation to the strategies used by linguistic systems for the distribution of grammatical information. Three types of transcategorial strategies are distinguished: “oriented”, “generic”, and “functional” transcategoriality. The status of linguistic categories is then discussed in the light of the analysis of these particular morphemes.