Metaphtonymy in Goossens (1990) and Geeraerts (2002) can be dubbed collectively as linear interaction. Non ⁃ linear interaction raised in this paper evades all defectives of its linear counterpart such as metonymical indeterminacy of componential elements, intermediate levels of inference, contradiction in inferring direction, and lack of reason in defining metaphors and metonymies. Non⁃linear interaction can explain more metaphoric idiom types such as “isomorphic but not motivated” and “motivated but not isomorphic” and support interactions inside metonymic idioms. Non⁃linear interaction is supported by both the Invariable Principle and the Conceptual Integration Theory.