The paper introduces a generalisation of the grammar formalism of Topological Dependency Grammar (TDG) (Duchier and Debusmann 2001). The result, eXtensible Dependency Grammar (XDG), is a description language for sets of labeled directed graphs. Lexicalisation turns XDG into a powerful dependency-based meta grammar formalism. As an instance of XTDG, we present Semantic Topological Dependency Grammar (STDG), a new dependency-based grammar formalism with a syntax-semantics interface to underspecified semantics.