I've touched on this before, but I'd like to bring it up again. The core of this being a third independent faction, though I wouldn't want to take away from Legacy of Romulus. I would however like to both expand, and alter the outcome slightly.
From the launch of Trek, the three big players from the Alpha & Beta Quadrants have always been the Federation, Klingon Empire and Romulan Empire. The Next Generation introduced the Cardassians, and they became the fourth big player into Deep Space Nine. With JJ's Trek, and Cryptic's Trek, both the Romulan and Cardassian factions are now only a shadow of their former selves.
I'd propose that those two shadows come together to form a true third faction. I wouldn't take away too much from the LoR story, except the episodes that have you aligning with the Federation or Klingons. Considering who D'Tan is, his message, and what the Republic stands for, I just can't quite accept that he'd join with the Klingons.
Regardless, Romulan and Cardassian Refugees; each having their own homeworld (think of it as two mini factions when you're starting up, though said mini factions later form a much larger, strong faction). Cryptic want to keep this Red vs Blue theme going, and that's fine. This proposed idea of mine would merely have the Romulans and Cardassians together, whilst not in conflict with the Federation or Klingon (instead they'd focus on the Tal Shiar and True Way).
Playable species would be (obviously) the Romulans and Cardassians, with Reman a C-Store/Reputation unlock. Bajoran-Cardassian Hybrids would be another C-Store unlock (unique trait) with the Suliban, Yridian, Paradan and Karemma as your other character/bridge officer contenders. I suppose you could throw the Jem Hadar in there somewhere too to keep everyone happy.
Keep your current Romulan ship line, and do the same for the Cardassians (1x ship until Tier #4 (where you'd get 2x)) then three ships (1x per career) at Tier #5.
Why is this a good idea? Because it kills two birds with one stone; it gives us the next big faction without the need to create another faction from scratch. The Romulans (lets be honest) are only half a faction as they stand. Create another half a faction (Cardassians) put them together, and you've got a third faction. Create another Fleet System (left of Iota Pavonis?) that would act as an embassy (of sorts). If players didn't want to have this alliance, they'd only need to play one side of the story.
I know this is probably a long shot, but I'd love nothing more than for STO to be a three-faction game, and I've never really been a fan of the mini-faction theme (which is where the Cardassians are going to end up if not this proposal). Besides the fact, the Cardassians are even less likely to align with the Klingons than the Romulans are.