I could rephrase the question as: how to segment content to comment on?
Looking at comment systems, it appears to me that comments are usually grouped around a specific piece of content; for each piece a different set of comments.
Facebook segments commenting per image, post, video, etc. Stackexchange segments commenting per question/answer. Medium is redefining how the split is done in blog articles by allowing to comment every paragraph/pictures in their posts (eg https://medium.com/about/8304190661d4).
On my site I'm allowing comments per block of content, but I'm afraid this would also segment conversations which could be about the general topic, and hence make it messy.