There are probably different kinds of discourse frameworks. I come to think of linguistic discourse analysis. In this framework discourses as "presidential addresses" and "newspaper editorials" are studied. The framework uses non conventional meaning clues, e. g. different points of view, inside the discourse with the semantics of conventional constructions in order to show how meaning is created in the discourse.
I agree with Hans - there are different approaches and one has to focus on a particulr discourse. For example, White House Briefings - see
The Linguistics of Political Argument. The Spin-Doctor and the Wolf-Pack at the White House
by Alan Partington
2002
DOI https://doi.org/10.4324/9780203218259
Something more general would be CDA (Critical Discourse Analysis - see the reader edited by Weiss and Wodak (Palgrave 2003)).
A lot of work has been done on Metaphor and Discourse (look up Andreas Musloff) .
Last but not least, "Corpora and Discourse Studies" eds Paul Baker and Tony McEnery (2016) or the earlier book by Michael Hoey, (2007). Text, Discourse and Corpora: Theory and analysis. A&C Black.