I keep forgetting the essential;
5) The return of Corporations would somehow implicate CS in both principles & features.
6) Buy/Sell, Economics, ratios, Banking, Investment.
7) Recession, Inflation.
8) Finance a War, still pay for Alliance, Subdue.
Anything else, anyone?
Maybe city-states could replace corporations to some extend in making resources more useful. You cold exchange resources for influence and boni with friendly or allied city states (on top of the additional boni)
Some examples:
Gift iron, horses, coal, oil or aluminium to a an industrial city state and every instance of a gifted resource gives you influence and production :+0,25

per resource from a friendly city state, +0,5

from an allied city state and +0,25

per turn from every gifted resource.
Gift marble, dyes or wine to a cultural city state and you recieve additional :c5culture
Gift luxury ressources to a mercantile city states to get additional
Gift strategic resources to militaristic CS and all combat units that require that particular resource receive a 5% combat bonus per gifted resource (you gift 3 iron, your swordsmen get +15%

. Might be a bit hard to balance. Maybe give +5% per resource until 15% and then reduce it to +2,5% for every additional resource.
Gift gold, silver, oil, aluminum or uranium to a scientific city state for additional

Bring back the former health resources: exchange cows, wheat, sheep or horses for

(keep it balanced: 0,15

per in all cities when friends, 0,25

when allied. Not sure about this one: there should be some other use for food resources otherwise there's no tradeoff.
It's basically reverse mercantilism: You export raw resources and import luxury goods, or machinery or weapons or whatever.
This should provide some interesting choices: build another Swordman or use the iron to improve my other units, or get a production bonus ? Some city states could give an additional incluence bonus for resources they desire for a short time.
Additionally, to make it harder to be allied with multiple city-states some of them should not only ask you to conquer their rival but demand trade embargoes: lose 0,5

from Ragusa per turn for every iron gifted to Belgrade for example. Providing rival CS with resources should drive their approval below 0, something that now only happens when trespassing or being at war, and other major civilizations shouldn't just scold you for competing for the favor of the same CS, but also for being too unpopular with their ally and to too friendly with their allies rival. This could create blocks later in the game and lead to cold-war like scenarios.
Ramkhamhaeng should be most likely to rely on a block of mutually friendly CS, while Alex would have the easiest time to be friendly with CS who hate each other.
Aditionallythere should be modiefied or new policies: United Front improves relations with city states who like a CS you're already allied with, a new policy in the Commerce tree -let's call it Free Trade- reduces the

penalty from providing rivals with resources etc.
That's my thoughts for now.