Users only being able to fulfill one goal per visit is incorrect. Not only would it be unintuitive if Google set Goal Tracking up this way, it wouldn't be a very helpful feature if it did work this way.
A goal is triggered every time a goal URL is reached. A common case we see on our site would be a user fulfilling the "Signup" goal, and then proceeding to fulfill the "Contact Us", "Purchase", or "Review" goals. We track these goal URL's via the Google Analytics JavaScript API.
If this is a behavior you are seeing on your site, it could indicate that you have set something up improperly.
**Edit: Fredrik is asking about completing the same goal multiple times per session. This answer was assuming he was asking about completing different goals multiple times per session.