It was an old video, in the latest stream there appeared to be no such option. Barbarossa only demands tea, not 1 tea or something. It pains me to say that but I think they are going with 4 amenities per luxury only for simplicity as well as a way to balance wide Vs tall. Coupled with rise of settler & district costs wide may not be as good as they sound.
I do think that they considered the option of multiple luxuries supporting more cities at one point though, which is supported by Marbozir video.
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I'm not sure this bothers the 'tall' vs 'wide', wrt if a lux only gives 4 amenities period, no matter how many copies you have.
IE -- have 2 unique luxs, that's +2 per first 4 cities. after that, it would shift to a mix of +2 and +1 per city, as you add new cities (to eventual +1 per city for 8 cities).
now, there's a list of amenity sources that mostly are driven by you:
Civics -- This is a direct player choice thing
Entertainment -- 'build the district or don't'
Great People -- not reliable, but player driven
Religion -- player choice, if you choose early enough
National Parks -- if you want less usable hexes in your territory.
So lets say you have those 2 lux from before. if you build an entertainment complex in your core cities, that shifts their needed amenities from lux based to entertainment based, and the 'new' cities all of a sudden have some extra luxuries to spare.
Tag on whatever civic choices are available (Classical Republic gives +1 amenity if the city has a district) along with religion, and your early game expansion can still continue. Ofc, hoping that you expanded in cities 2-8 to add more unique lux on top of the starting 2 you had - or extra to trade with an AI that has extra.