Is it considered bad manners to answer a question that already has an accepted answer with a different response?
There is a lot of interest in the meaning of "accepted answers" on Meta.Stackexchange. Generally, the wisdom seems to be that multiplying good answers to questions (even if they have an accepted answer already) is something that enriches the SE sites, and makes the internet a better place.
Don't add trivia and drivel. And don't repeat what is already clearly (and correctly) stated in existing answers. But if you believe you have new information, another angle, some additional insight, then by all means add a new answer, even if an "accepted answer" exists already.
Here are a couple more Q&As which might help:
No, not at all — as long as you have a reason to do so. The accepted answer mark is really just the original poster saying they think they are satisfied, but there is usually room for improvement. Maybe they don't know what they are missing. And even if they never come back to the question, think of all the other visitors that may read the posts.
- Is the existing answer wrong, misleading or otherwise faulty?
- Do you have more information to add not found in other answers?
- Do you have more in depth analysis of the topic that might benefit some readers?
- Can you present the (complete) answer in a more clear or accurate way?
If the answer to one or more (preferably more) of those questions is yes, then by all means answer. There is nothing bad-mannered about posting better answers to existing questions. In fact that's one feature that makes SE sites more useful than some other discussion forums on similar topics.