Let's say, I've posted a solution to a puzzle and it's been accepted. Later, I think of an alternate solution, distinctly different than the first but (hopefully) meriting mention.
Is it better to make an addendum to the original, accepted solution or post a new answer which can live or die on its own?
The stipulation that the first answer has been accepted isn't necessary but it might influence whether or not the original should be left alone.
Of course, a third possibility is to just ignore the alternate solution and hope that someone else posts it.