Actually, "very powerful entities" just has to be tweaked to include 'very powerful Events and Forces' to apply to a historicalish 4X like Civ:
The Industrial Revolution introduced an entirely new social/population class, the Industrial Worker, which took a century or more for governments and societies to come to terms with (if then), and it up-ended politics and society and led to the 'Ideology' crisis that wracked the early 20th century with warfare.
Ideologies, already used as an excuse for disliking your neighbors in Civ VII, could be expanded to show their real impact, as they warped governments and societies both. While the impact of Fascism and Communism were obvious on Germany and Russia, FDR's New Deal of government intervention in the USA was almost equally radical, and a new American civil war or revolution was avoided by a smaller margin than is usually suspected.
The growth of and interdependance of Governments and NGOs (Non-Government Organizations) is nothing new, but getting more intrusive recently: international bankers and traders started warping government decisions by at least the 15th century CE, and kings and governments borrowing from international bankers and then not paying their debts brought massive instability to both governments and the banks. And the series of financial 'crisis' events occurring almost like clockwork since the early 19th century that disrupt society show that no government controls them, no matter how they 'tweak' their control over their economies - there are too many Outside The Government factors at work
The impact of humans on the planet expanded and accelerated in the past century, and even if the overall planetary impact is ignored (as many are attempting to do today) local impacts have been massive in things like the Dust Bowl in the USA or the on-going drought and starvation in north-central Africa. Climate Change, even temporary, has been a factor in human settlement since the beginning of the Neolithic, with major disruptions or contributions to making the disruptions worse for societies and governments from the 5th to the 17th centuries CE.
So there are a lot of ways to provide an End Game Crisis or set of calamities to challenge the gamer - some on-going throughout the game, like the planetary or semi-planetary climate/ecological variations, and some Unique to the late game as individual Civs and governments become more susceptible to Outside Factors they cannot ignore.
If you want a sort of "end game crisis" system, you could set it up I almost want to say more like the Colonization end game, where basically you get to a certain level, and then you basically "claim" your victory, but then you have a set limit afterwards to "prove" your victory (there it was working towards declaring independence, and then having to fight).
In civ terms, the 2 that make the most sense to me as potential "victory conditions" would be for military and space. For military, maybe when you get to the modern era, and have accumulated those points towards the Ideology track, you can be given the option to basically declare a World War. When you do that, I think every civ should either ally for you, or declare against you. Everyone who declares against you will immediately ally together. The opposition could be given a level of free units, bonus to building military units, bonus combat strength, etc... (maybe they get "crisis" policy cards to decide). I don't know exactly what the victory conditions should be there, maybe you just have a target number of settlements you and your allies need to conquer net of your current status. Or maybe it's a "hold on to what you have for the next 20 turns".
For science, you could trigger it after the satellite launch, and basically create a "Space Race" victory. You could set up a number of projects and criteria, and basically create a challenge to be the first civ to land on the moon. Other civs would get some bonuses to building their aerodromes/launch pads.
Not sure what econ/culture would be..
But in each case, basically you need to build out to not just be the first civ, but you potentially need to be well ahead of the game, so that when the others get their bonuses, you can hang on. So like I'm way ahead in my game, but if every AI civ was given 2 free commanders, +100% production to building military, and +10 combat strength on all their units in their home territory, would I still have enough power to conquer the world?