Star Trek 3 co-writer J.D. Payne spoke at the LDS Film Festival last month and revealed a few details about their mindset for the third film. He doesn't give any story details, but he does discuss what the themes of the story could be.
We're trying to set up a kind of situation where you really could — and not in just an 'everything's relative' sort of moral relativism — you could be a good person of any creed or philosophical background and come down on both sides of how you should respond to this opportunity that the crew has.... that also has some pitfalls to it. Where you could argue very, very, very compellingly that 'this' is what you should do, and if you're advocating 'this' then it's actually evil.
It's sort of the Adam and Eve thing, where should we eat the fruit or not eat the fruit? Well, there are some very compelling reasons why they should and why they shouldn't. So, similar kinds of things here that really give the whole movie and opportunity to sort of play with that, and have people come down on different sides and wrestle with it; then come to an ending where you can walk out and say, 'You know, I don't know what I would do.
It definitely sounds like they are looking to spark some good discussions among the fans. He also says at the time that they've pitched the story to Paramount and they are by now working on the first draft of the script, which he thinks will be done by May. Thanks to TrekCore.