The aim of my talk is to offer a dialogical interpretation of non-normal modal logic which will suggest some explorations beyond the concept of non-normality. This interpretation will be connected to the discussion of two issues, one more philosophical and the second of a more technical nature: namely a minimalist defence of logical pluralism and the difficulties involved in the application of the so-called Hintikka strategy and hybrid languages while constructing tableau-systems for non-normal modal logics.