More advanced material can be found from Stephen H. Levinsohn. Analyzing Discourse: A Manual of Basic Concepts, which he coauthored with Robert Dooley, is one of the best entry points that I know of (after Runge) into their approach to discourse analysis and information structure. Levinsohn and Runge tend to follow an (eclectic) functional, cognitive, typological linguistic framework that would be broadly shared by many linguists, including Randall Buth. Levinsohn and Dooley have made their Analyzing Discourse available for free online (although note the disclaimer: "May be reproduced only for non-profit educational use.") http://www.ntslibrary.com/PDF%20Books/Analyzing%20Discourse%20-%20A%20Manual%20of%20Basic%20Concepts.pdf
From there, Levinsohn has many other materials on his SIL page, including his Discourse Materials for Narrative an Non-Narrative Discourse and BART Displays Enhanced for Discourse Features.
https://scholars.sil.org/stephen_h_levinsohn
https://scholars.sil.org/stephen_h_levinsohn/discourse
https://scholars.sil.org/stephen_h_levinsohn/bart
He provides a brief overview of some key discourse features in BART Displays Enhanced for Discourse Features: Greek New Testament, although it depends on his other writings.
https://scholars.sil.org/sites/scholars/files/stephen_h_levinsohn/bart/enhancedbartdisplaynt.pdf
As I understand, he's been working on an updated version of his book dealing explicitly with the Koine Greek of the NT, which hopefully will be released someday, Lord willing! That would be Discourse Features of New Testament Greek: A Coursebook on the Information Structure of New Testament Greek.
https://www.amazon.com/Discourse-Features-New-Testament-Greek/dp/1556710933