The interaction between metonymy and grammar is commonly understood, in keeping with the classical cognitive linguistic doctrine about cognitive operations motivating linguistic structures, as unilateral – conceptual metaphor and metonymy shaping the grammatical system. However, we argue in this article that one of the possible corollaries of the Equipollence Hypothesis (Mairal & Ruiz de Mendoza, 2009; Ruiz de Mendoza & Luzondo Oyón, 2012) covers a truly bilateral interaction between grammatical structures and cognitive processes. The Equipollence Hypothesis is shown to allow for grammatical phenomena facilitating or constraining, i.e. blocking, the application of conceptual metonymies and their expressions across domains of linguistic inquiry. Specifically, we show in four case studies that grammatical constructions may actually pre-empt lexical (and grammatical) metonymy.