This paper describes the extension of the Ontologies of Linguistic Annotation (OLiA) with respect to discourse features. The OLiA ontologies provide a a terminology repository that can be employed to facilitate the conceptual (semantic) interoperability of annotations of discourse phenomena as found in the most important corpora available to the community, including OntoNotes, the RST Discourse Treebank and the Penn Discourse Treebank. Along with selected schemes for information structure and coreference, discourse relations are discussed with special emphasis on the Penn Discourse Treebank and the RST Discourse Treebank. For an example contained in the intersection of both corpora, I show how ontologies can be employed to generalize over divergent annotation schemes.