Currently, the "add another answer" button only appears if you've already answered the question. How about putting it on if there's already two answers? This would help fend off people who register just to put a "thank you" or a "me too" answer as comment.
Why would "Add Another Answer" deter those posts when "Post Your Answer" doesn't? I don't think it would change anything; "another answer" just reminds you that you've already answered