Currently the system detects duplicate answers from the same user and flags them for moderator attention. This is useful, but could be streamlined.
Duplicate answers fall into two main categories:
Answers to duplicate questions that haven't been closed yet (or even attracted a single close vote/flag).
In the first case there is absolutely no benefit from having multiple spam posts - except perhaps to confirm that the user is a spammer rather than just misguided.
In the second case the user probably doesn't understand the system so preventing them from posting and telling them to flag the post as a duplicate is educational.
If the user gets this message and then posts a different answer to the same question then this should be flagged as this would indicate they are trying to get round the system in some way.
There are occasions where the same basic answer can apply to different questions, but in those cases the actual answer posted should really be tailored for the specifics of each question and therefore the actual answer won't be identical.