The type-theoretic modelling of DRT that [degroote06] proposed features continuations for the management of the context in which a clause has to be interpreted. This approach, while keeping the standard definitions of quantifier scope, translates the rules of the accessibility constraints of discourse referents inside the semantic recipes. In this paper, we deal with additional rules for these accessibility constraints. In particular in the case of discourse referents introduced by proper nouns, that negation does not block, and in the case of rhetorical relations that structure discourses. We show how this continuation-based approach applies to those accessibility constraints and how we can consider the parallel management of various principles.