This paper makes two generalisations of categorial calculus of discontinuity. In the first we introduce unary modalities which mediate between continuous and discontinuous strings. In the second each of the modes of adjunction of the proposal to date, concatenation, juxtaposition and interpolation, are augmented with variants. Linguistic illustration and motivation is provided, and we show how adherence to a discipline of sorting renders the generalisations tractable within a particularly efficient logic programming paradigm.