Here's my 2cents on running a massive empire. I recently won a game as Rome with a 20+ city empire. Your two biggest concerns for having an empire that big will be your treasury and happiness. Science will follow naturally, and culture you'll always struggle with a little. Here's a snapshot of that game.
Luxuries
One nice benefit to a big empire is that you'll probably have access to loads of those happiness-providing luxuries. But that won't be enough! See below.
Policies
- I added in some piety. The benefits to happiness and culture definitely helped early on.
- I personally invested heavily in the honor branch. One of those policies allows you to gain 1 happiness for garrisoned cities. When you're talking about 20+ cities that's actually really significant.
- Later on I invested in commerce to get to Protectionism. That extra happiness from luxuries will keep you in the green.
- Finally I put a toe in the order branch and autocracy branch. The unlock benefit from autocracy was my last pick and frankly it was enough to get me thru the end of the game. It really helps with unit maintenance.
Specialization
With a big empire you can afford to have some specialist cities. I had one GP factory that kicked out a GP at a decent rate. Golden Ages are HUGE in this game! I can't emphasize that enough. You can go from running in the red to +300 gold/turn during a golden age. Save a GP to pop a golden age for budgetary emergencies.
Unit Maintenance
Now with happiness in order, I start to run into treasury deficits from unit upkeep. Delete any workers you aren't using! For garrison-happiness, I built low-hammer obsolete units in the modern era like Lancers. I think of them as my royal Honor Guard
Even middling production cities could build them in under 10 turns.
Buildings
Don't build a building you don't need. It's as simple as that. Don't put walls around cities deep in your empire and don't put armories / barracks in cities that won't ever produce units. If you run out of things to build it's pretty worthless to put toward "wealth" since it may net you +1 gold / turn. You're better off putting it toward a wonder even if it will take 60 turns. If someone beats you to it, you get a cash bonus!
The Art of War
You won't have a big empire without taking out some neighbors! Fortunately you're war-mongering should earn you enough cash to stay afloat. Pillage, sack, and repeat. Always puppet your cities if your happiness hovers too low. Annex key production cities, set the population to production focus and prioritize courthouse ASAP. Don't do more of 2-3 of these at a time. If left to their own devices too long, a puppet will bankrupt you with stupid buildings that don't help you long-term but cost a lot in maintenance. I think of it as their form of passive resistance
If a city is too small and too fringe to be any benefit, especially if it lacks a needed resource, don't hesitate to put it to the sword.
Conclusions
I know there are probably a lot of policy strategies that will emerge, so I don't claim to be any kind of expert. All I can say is my approach worked pretty well and it was exciting! There was never a time where I was always set-for-life on either happiness or gold. I always had to juggle some aspect of it and the new culture policies always seemed to arrive just in time. I'm sure a better "big money" strat will emerge in time.