Suppose I give a solution to a problem in an answer and then later on I think of a different method to solve the same problem.
Should I edit my old answer and include the second method, or should I add another answer?
I don't think I've ever seen a user give more than one answer to a question, but maybe they should have.
If the second answer is of a different nature, using different tools, etc, I would say there would be no problem adding a second answer. However, if the second answer is simply a slight change to the original answer, I would incorporate those changes into another section of that answer.
Of course there are shades of grey involved here and others may feel that a separate answer is too close, so don't be too surprised by some downvotes. You can always improve the second answer by adding some different ideas or methods to it.
One reason against distinct answers is that they might seem like attempts to gain more reputation for answering a single question. But in those cases where two answers means approximately twice as much work as a single answer would have been, I have no problem at all with that kind of reward. And having multiple answers allows independent voting on them, so this is a great way to let the community decide which of them is more useful.
I'm using this approach myself, with some posts here on Math SE, and several posts with multiple answers on Stack Overflow, sometimes with interesting vote distributions.
