You can write multiple answers and each answer can gain its own reputation for you. You will of course be limited by the rep cap of 200 per day.
As for when it is appropriate, two such situations that I have seen it used for on multiple sites are:
- When one posts answers that are mutually exclusive. That said a question that elicits mutually exclusive answers that are equally valid are usually (but not always) POB(Primarily Opinion Based).
- Breaking up extraordinarily long posts. Ridiculously long Facebook feed length answers get hard to read. People may give up part way through. The use of markup is your friend in such situations to add some visual variety, but it isn't always enough. By breaking up the answer and making it more reader friendly, you are doing everyone a favor.
I wouldn't write two answers lightly though. The first question I would ask myself is: Is there a reason to separate these answers? If not, then don't. If yes, whether your reason is one I listed or one of your own proceed with caution. No matter how good your reasoning you run the risk of catching downvotes from people who are voting on your perceived gaming the system rather than your content. It is also important that each answer adds value and can stand on its own. If the other answer is removed, will the answer still stand? And vice versa?