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Despite some rather glaring plot holes, I very much enjoyed the Trek reboot and have seen it twice. A sequel has already been greenlit, and the good folks at SFSignal wasted no time asking what the first Trek reboot sequel should be about. Here's what I suggest.
What I'd really like to see (barring the possibility of an ongoing TV series with the current cast) is an actual, ethical/moral dilemma, which is what Trek has always been about. Moreover, I think you can get that done based on what happened in this film.
We know that the Federation has lost a founding member in Vulcan, that Starfleet has basically lost an entire Academy class and a half-dozen ships to Nero, and that the Klingons lost an entire fleet to the rogue Romulan. Everyone in the galaxy knows that A) there's something called Red Matter that can make black holes, which is every bit as dangerous as the Genesis Device ever hoped to be, and B) that in a little over a century, Romulus is going to get obliterated by a supernova.
Basically, Romulus has the motive and the opportunity to finish what Nero started and take out both the Klingons and the Federation. They don't have the luxury of waiting this out, both because someone else might develop Red Matter before they do, and because unless they have an invincible position in 129 years they'll be at the impotent mercy of their enemies.
You could do a great non-proliferation allegory as the Enterprise has to forestall all-out war with the Romulans and Klingons and prevent anyone or everyone from getting their hands on Red Matter, possibly by kidnapping Spock (who, one assumes, can make it if his future self figured out how) or tracking down the new, presumably hidden Vulcan survivor colony where future Spock is hanging out.
You can some of those great Kirk/Spock/McCoy ethical debates about whether what the Romulans are doing is moral, whether now would be a good time for a preemptive strike against the weakened Klingons (and if such a thing is ethically defensible), if the Federation should compel future and/or present Spock to create Red Matter as a deterrent--all while enjoying some great space battles and chase scenes as the Enterprise stands alone between the entire Romulan Empire, a bloodied and enraged Klingon Empire, and all-out, galaxy-consuming war.
Just my wish list, anyway.