Is not liking the answer given for an existing question a reason enough to ask a duplicate/similar question? Ironically, kiamlaluno did not receive an answer on asking this.
Not liking the answer is an insufficient reason to justify a duplicate question. The question should be closed as a duplicate of the original question and the original should be improved if necessary. Editing a question will attract more attention to it. If the question has an accepted answer, posting a bounty is a more effective means of attracting new answers. That is the desired course of action.
In rare cases, the duplicate question might be considered more useful or helpful than the original question. In that case, a Meta question posed to the community about closing an older question as a duplicate of a newer, clearer question might help to determine the correct action. However, generally speaking, we would prefer to see old, canonical answers improved rather than new posts.
So if you don't like the answers given:
1. Edit the original question to make it better
2. Post a bounty on the original question
Otherwise, your duplicate question will probably be closed as a duplicate and someday in the distant future, it will be merged with the original question.
That said, it is not helpful to anyone to close a question as a duplicate of a closed question -- if they are duplicates, then it should be closed for the same reason. If the close reason doesn't apply, then it's probably not actually a duplicate. Also, it is not helpful to close questions as duplicates of posts with negative score, since this are auto-deleted at some point in the distant future, which will break the duplicate link.