Well, since this is kinda a wish tread (albeit not inside the realm of the impossible, considering how some civs have been heavily modified such as Arabia and France) there goes my suggestions for remodelling already existing civs (plausability be damned

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America
UA - We the people: +1 extra sight to all units. Ideological tennets unlocked at Economics, you start with one additional tennet of your choosing whenever adopting a new ideology (it will add to the tennets, rather than just "filling" them, a la Byzantium's extra belief).
UU: Pioneer. Replaces settler, minutemen. +1 extra sight and movement, 25% cheaper to build. Can defend itself (same strenght as a scout). They can be consumed to reclaim enemy non improved tiles adjacent to your territory (this will cause diplomatic tensions with the civ, tough)
Comment:
"We the people" makes the US a late era powerhouse, while playing with the new ideological tennet system in order to give the American UA a little tad of much needed spice. In terms of favour, the idea is to represent the US power based more on the strenghts of its political system (which was quite advanced for its time) rather than on economy or science per se, which also allows for a quite flexible type of play.
However, the "fast expansion America" and its historical advantage of being able to gobble vast swaths of land is still present trought the pioneer unit, allowing you to employ an agressive, easier expansion due to reduced costs of this settler unit and the lack of need for protection, making it possible even to snatch enemy territory trought a short of "mini culture bomb" mechanic. This will make the US quite apt at horizontal type of expansionist games, and will put them in a collision course with vast land gobblers such as Russia or the Soshone (hello realism!

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Japan
UA - Sword, mirror and jade
-50% to ideology related unhappiness, great generals and admirals can be consumed in order to generate a Japanese artifact (ex: "Japanese classical era armour")
UB: Dojo (replaces armory, zero fighter)
Units built starts with the "bushido" promotion. +1 XP to new units for each culture point that the city generates. It has one extra slot for great works, new Japanese - exclusive theming bonuses added for this building
UU: Samurai (improved)
It has all its previous statuses, plus a new promotion: "strategy: unit +100% more likely to generate great generals, unit ignores the enemy's general bonuses".
Comment:
The new Japan is designed to result into a not too much typical combination: a military and cultured type of civ, with each aspect strenghtening the other. Both its UB and UU is geared towards war and a higher production of great generals, while its UA allows Japan to take advantage of this "excess of great generals" and turn them into cultural artifacts.
In addition to that, its UA allows Japan to be able to better resist ideological preassure on the modern times, thus greatly rewarding having a stronger culture and making you able to pursuit whichever ideology you prefer regardless of the pesky foreign influence, making yet again your culture help your war efforts and vice versa.
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Celts
UA: Duidric Lore
Cities next to unimproved forests have +1 happiness, +3 if they are near 3 or more unimproved forests or a natural wonder
UI: Burial mould (replaces ceydic hall)
Tech prequisite: None
Can only be built on forest tiles
Can only be built on the ancient and classical eras
They cannot be built next to each other (for balancing reasons)
+2 base faith, +1 faith per passing era, it can be digged like an archeological site with the arrival of archeology (and thus, replaced by eithe a relic or a conmemorative site)
Comment:
A new take on the celts, the idea of the Burial mould is to provide the celts with an early and steady source of faith, but making it able to extend its use pass the early "race for religion". Making it tie with the archeology system would make for a fun improvement planning, me thinks.
The revamped UA, however, is designed in order to make the celts able to expand and grow faster than usual (they were a quite popullous civilization / cultural group), with the added twist of keeping a different strategic factor to city placement relying on forests / natural wonders.