The class of mildly context-sensitive languages is commonly regarded as sufficiently rich to capture most aspects of the syntax of natural languages. Many formalisms are known to generate families of languages which belong to this class. Among them are tree-adjoining grammars, multiple context-free grammars and abstract categorial grammars. All these formalisms have in common that they are based on operations which do not copy already derived material in the course of a derivation. We propose an extension of the class of languages captured by these formalisms that is arguably mildly context-sensitive. This extension is based on a mild use of a copying operation we call IO-substitution.