If you haven't already done so, I suggest reviewing Editing Help in the Help Center, as it covers some of this.
The cardinal rule for me is that you should not change the meaning of an existing answer.
For instance, you should not remove the word "not" from this answer, because it would change the meaning.
Things like updating broken links and fixing spelling and grammar are OK.
Adding new information is a serious gray area, though. This does run the risk of changing the meaning of the answer. I find it usually best to leave a comment with the additional information, and leave it up to the person who answered as to whether they want to incorporate it.
One example where I would find this acceptable is: an answer recommends using some command with a specific set of options, and your additional information explains what the options do.
If your own additions can stand alone as an answer, then by all means post a new answer.
Finally, don't be too afraid to edit; if it turns out to be really bad, either the original author, or 2K+ community members, can roll it back.