My paper got accepted for publication last week, and I have not received the galley proof yet. I recently learned that one of my results implies another interesting result, and I want to mention that in my publication. Deriving the new result takes no more than three lines, and I do not think it can be published on its own. Can I ask the editor to add a new result to an already accepted paper?
I strongly suggest not doing that.
- If the correction will be accepted, it is a sign of "the editor is accepting non peer-reviewed results ---> paper is questionable", unless the editor is a proven expert in your field (and even then, it is obviously not a blind review and the editor has some interest in the accepted paper being finally published).
- if the correction will be submitted to peer-review, the paper will go back to peer review.
You can certainly ask the editor. But, the most likely outcome is that the paper would need an additional review. I doubt that it would require starting the process over again, but the editor, unless they are already an expert in your subfield, would most likely ask advice of one or more of the original reviewers.
It would delay your paper's appearance, though perhaps not for long.
The alternative is to take the new results and incorporate it into some new paper with additional results, since you say it isn't enough to stand on its own. But others are fairly likely to notice the extension in the meantime, so you might get scooped on it.