In particular, I'm reviewing this answer. Is it kosher for other users to add content to the original author's answer? I almost feel like this should be another answer, although if it contains duplicate content, I can see the reasoning for combining the two.
Is it kosher for other users to add content to the original author's answer?
Well, yes, it is. That's the whole point of suggested edits on posts (including answers).
If the edits improve the answer, approve them. If they don't, don't. If you don't know if the answer is an improvement or not, use "not sure".
In cases where the edits completely change the answer, I would probably reject (in particular if the answer already has been voted on).