@Boris Gudenuf : I agree that a complex system could be developed for luxury resources, with changes occurring through the ages, etc. But all I'm suggesting as a starting point is a slight variation on the current system. right now, a luxury resource provides amenities to 4 cities max, with all excess being generally useless. For now I'm just suggesting something 'simple' - instead of one lux per mine giving four cities amenities, have luxes produce a number per turn [specific amount would have to be tested, but maybe 4 per turn so it still provides for the same amount of cities if they use 1 per turn]. If you only have 3 cities, then you would only need 3 per turn. You could either stockpile the difference for use later or sell/trade to another civ. I think this improves on the current amenities system; and it actually makes trading easier [don't have to remember which resource you're already receiving in a trade or when a trade ends - something I now track separately while playing]. It also limits the artificial distinction where only four cities ever want one specific luxury. Might have to change the number produced per mine for balance; but I think this could be worked out with a little testing.
Okay, Understand. I freely admit that one reason I looked for something more 'complicated' (reading My Desires into your OP, Mea Culpa) is that I would like to see the artificial distinctions among Resources abolished: a resource would be amenity, strategic, or 'bonus' based on situation, technology, and possibly even Civic (culture) and the exact use of a Resource would change throughout the game.
For instance, Horses might be a Strategic Resource in the first 5 Eras of the game, but along about the Industrial Era they could also be used for Race Tracks, which would be Amenity-Producing Improvements or Buildings - extending the use of the 'Strategic' Resource after horses lose their military utility.
Likewise, Cotton might be a Luxury in early Eras, but Cotton combined with the first Factories and Dyes produced Cheap Cloth, a major Gold-Producing manufactured Good that really spurred the growth of the English Trade Empire of the 18th century.
In other words, I'd like to see at last as much Accumulative Necessity for 'Luxuries' as there is now for Strategic Resources, as a step towards an Economic Overhaul of the game (3rd Expansion or Civ VII, I can be patient).
So, for instance, for an 'Interim' complexity, initially each Point of Resource could apply an Amenity Bonus to 1 City. Cities with a population of, say, 6 or more would require 2 points (exact numbers to be determined by testing, ideally), 12+ population 3, etc.
If you have a seacoast literally crawling with Turtles, every Population Point in your civilization might be feasting on Turtle Soup, but more likely each city would have a slightly different 'mix' of amenity-producing Resources.
I would even make it possible for you (possibly with a given Civic or Policy Card) to purposely 'withhold' some amount of Luxuries so they could be used for Trade (or bribes!) instead of keeping your people happy/Loyal.
All of which would provide much more flexibility to the Trade system, as you would now be, like Strategic resources, trading specific amounts of Amenity Resources in the same way - a batch of 1 'point' or more at a time, or a continuous number of points per turn, and, frankly, if you were providing a considerable number of points of Luxuries per turn to a Civ, it might be very dangerous to that Civ to attack you and temporarily cut off the supply, especially if he's got a bunch of 15 - 20 population cities and few Luxury/Amenity resources of his own. That, in turn, beefs up the Diplomacy system a bit, since Bribery With Amenities becomes a much more (potentially) Lucrative process, and withholding or offering Amenity Resources by quantity should garner a Civ some major positive attitudes even from the schizophrenic AI.