Title sums it up, could any of you see a future where a number of the known major races of Milky Way (Klingons, Romulans, Cardassians, Ferengi) would join the Federation? Or perhaps, due to the size of the Romulan and Klingon empires, a merging of the major powers? I don't just mean an alliance, but a full joining of the Alpha and Beta quadrant powers.
If yes, then perhaps detail how you think the arrangement would work. If no, explain why this kind of "Galactic Federation" could never exist.
EDIT: Going even further, could you see even the Dominion races joining? FYI, I've only seen TNG,TOS and all the movies, so my knowledge of lore and information shown on DS9, VOY, and ENT is spotty at best.
Qapla'!
I'm assuming you are meaning the prime universe.
Klingons: If as presented up to DS9, I doubt the Klingons would accept a government like the Federation: they are still too warlike and I would doubt the Federation would even accept their application without major changes the Klingons would likely not accept anyway (IE term empire implies they still conquer territory and subjugate people). The Klingons also still seem xenophobic when it comes to government (they slam humans at every turn as being to weak, criticize anything that isn't the "Klingon way"), and I don't see the Klingon High Council being subordinate to the Federation, or the Klingon populace allowing it. I think the best that could be hoped for is an alliance between the two. The Klingon Empire is too large to be absorbed, being nearly as large as the Federation, with a government and military as strong, so I don't see the Klingons needing to be part of anything other their own empire.
Romulans If after the destruction of Romulus and Remus, I think it is conceivable the Romulans would consider becoming part of the Federation.
They have these things going for it:
1. The worlds that have been subjugated by the Romulan Empire (as with Klingons, this implies they conquer other worlds), without a central government, Romulan forces would splinter without a strong leadership to unite them, and many worlds might just rebel and regain independence.
2.The Romulan government seemed pretty oppressive, and even common Romulans (based on Unification) seem to always be looking over their shoulder for the Tal Shiar. With the seat of that government destroyed, I think maybe the Romulan people remaining on other worlds, along with the worlds they oppressed would throw off the yoke of the Romulan Star Empire.
3. The Federation would likely extend a hand to help survivors of Romulus/Remus, and gain good will from the remnants of the Romulan Empire, as well as the worlds no longer under their domination.
4. I think Vulcan in particular would be likely to try to help their Romulan cousins. If the movement started by Spock still survived the destruction of Romulus/Remus, it is conceivable that the surviving members of the Romulan race would finally see the illogical effects of empire, and how it brought about the destruction of their world. Perhaps enough Romulans would embrace logic and the Vulcan way, if not to be like Vulcans, then perhaps more peaceful and willing to accept a way of life in line with the Federation. As for the conquered worlds formerly under Romulan Empire control, it would be literally a case by case basis.
Cardassians: If as presented up to the end of DS9, it seems that Cardassia's government had collapsed, and Cardassia was essentially destroyed, not unlike Germany after WW2. Whatever worlds Cardassia had conquered were likely no longer under their control. I can see a scenario where the Cardassians see the mistake of having followed leaders like Gul Dukat and the Dominion, rejecting the idea of empire, and with both Bajor and the Federation leading efforts to help rebuild Cardassia, I can see where the Cardassians would be open to joining the Federation.
Ferengi: Kind of depends on how well the Ferengi accept reforms instituted by Rom. Despite their greed, the Ferengi don't seem warlike, and really not all that incompatible with the Federation. The biggest obstacle besides their system of unfettered and pure capitalism, is how they treat females, but it seems that under Rom, things like that will be reformed. But if a Ferengi like Quark can change as he did over the course of DS9, I think it is possible that if the Ferengi became less obsessed with profit, it's possible they would one day join the Federation.
Dominion worlds: A little more complex here. The Dominion surrendered to the Federation in an effort to end the war, meaning they would no longer come across the wormhole to fight. It really didn't say they would merge with the Federation. I suppose by having Odo become part of the Link, the Founders would have a better understanding of solids and the Federation, and may be persuaded to take the treaty ending the war one step further and even cooperate with the Federation, but I think there is too much left unknown, as to whether they would join the Federation. I tend to think the Gamma quadrant is too far from the Federation with the Wormhole being the only connection, for the Dominion worlds to want to join. The biggest problem I have is the Founders are literally seen as gods by the Vorta and the Jem'hadar, who are the enforcers of the Dominion, literally genetically engineered to follow the Founders's will and see it done. That in of itself is an action the Federation would not allow, and would require the Founders to abdicate their status as "gods." Also, while Odo's influence may change the Founders' view, there is also the double-edged sword that maybe Odo would be changed by the Link. What if Odo's idea of joining the Link to "teach" the other Founders about his experiences is rejected, and they change Odo as a result to be more like them?
SO, I think the best we would see is cooperation between the two powers, namely when the two sides open up a trade, or when one side crosses the wormhole to explore on the other side.
As to the Breen, Gorn, Tholians, Orions, or some other antagonistic governments, I don't think they would want to join. Individuals, maybe, but not en bloc.