If your proposed answer adds constructively to (and differs enough from) the existing content, either:
- go ahead and post an answer, irrespective of whether the existing answer is upvoted, accepted, etc., or
- ask the OP to add the things you'd like to have in the answer, and if they can't, or didn't after a reasonable time, add your answer.
What I'd do in such a case is comment first. I know editing to improve answers is the way of life in SE, but making large scale changes to another's answer makes me uncomfortable, especially since my edits won't go through review. If the OP then gives me the go-ahead, then I make the edit.
I should stress that this is an opinion. I have had some of answers go through substantial improvement, in one case by the poster of the question, improvement that I have welcomed. In some cases I have resisted change, if the resulting answer might become too unwieldy. I personally prefer different answers addressing different viewpoints, even if they present the same method.
@hbdgaf is spot-on in that minor changes should be edits.