I keep wanting to use the share-my-own-post-and-add-more feature the way I use replying to myself on Twitter and Mastodon. It doesn't really work here, though—the original post takes center stage and whatever comes after it is (often far) below the fold—and I need to break that habit.
The obvious replacements are “just don't do that; make a new post ex nihilo”, which establishes no connection to the context of the original post, or “edit the original post”, which is a little bit revisionist and doesn't surface the new content to followers.
Cohost doesn't really have a good answer for this yet. It seems more designed for posting finished, complete content.
(I don't remember how Tumblr addressed this. I never did become a particularly active Tumblr user, so 99% of my Tumblr experience is looking at screenshots posted on Reddit and later Twitter.)
Suggestions welcome.