This is my default fantasy setting, Arth (details here and here).
It revolves around The Elven Empire and its domination of all areas in the Known World. The High Elves are on par with Upper Tier Justice Leaguers; so the Elven Army is about 60 of them that scry, gate in, dominate, and move on. The Dwarves and its community of Halls were pacified by three of them over the course of a few weeks when one of them destroyed an entire hall that swore to always fight the Elves with a flick of her wrist. The Low Elves then go in and set up some administration if needed, but mostly as long as tribute is given and the laws of the Empire are followed the locals can do pretty much what they want. If needed the Governor will call in an Army member or two and eliminate anything that might be a problem. While they try for a gentle approach, they are not above just eliminating everyone in an entire biome or two and starting over. The only problem is that The Empire runs on Elventi Time. So every 10 years or so, rulings come down.
Humans are notable in the setting because there are just so darn many of them, they are willing to live anywhere and do just about anything, and they make great client states. Also note the Elves saved their entire species from the Waptinti killing them all off. The Elventi upgraded Human civilization by a couple of developmental stages... (after using them as laborers... to pay their way). So humans are just there, following The Ways, in their local biomes.
I haven’t, if only because it is hard to get around the “why don’t they just solve the problem.”
So I think the trick would be to have a tri-continent set-up and a bipolar power structure and set it up Cold War style.
If the Elves and Dwarves were to ever fight directly, it would likely be the end of the Age. And they both know that.
However, a large amount of Mithral, a resource they both depend on, has been found throughout a third continent. Now that third continent has always been a source of contention for both of them, however, the humans that lived there were too numerous to make it worth conquering directly.
So now you have a gold rush, and both great nations trying to act through intermediaries to gain access to valuable resources and to keep the tensions just this side of going hot.
I've seen some examples where humans are said elder race. For instance Netheril from the Forgotten Realms was a human magocracy that justifies a lot of setting lore while having destroyed themselves long ago in a war against some obscure enemy.
While not a tabletop rpg, Geneforge has human wizards serve as the creators of fantasy monsters such as dragons. You generally play as one such wizard, known as a Shaper and the plot is based on these new species fighting for the right to self-determination.
I wrote a few thousand words on a setting like this a long time ago. Essentially, humans and the elder races swapped places. The premier powers were elves, dwarves, goblins, and orcs.
Humans used to rule the continent, until the orcs, who they’d created by injecting slaves with demon blood, and elves, who lived in traditional asshole-under-the-hill-who’ll-steal-your-children style and kept getting pushed back by humans because of it, rebelled. Humanity now exists primarily as elven vassals or scattered tribes looking out for themselves.
Orcs ruled the southern half of the continent, and elves ruled the north. They were locked into eternal war, with the elves going all steampunk industrial and the orcs breeding new and more outlandish forms of orc. Orcs can breed with anything, just like demons, so a lot of the animal people races are just weird kinds of orc.
The first dwarves were elves who were infected with a strange parasite and left stunted and weak. The elves tried to wipe them out, but they survived by escaping into the mountains, where they got even more industrial, reaching Iron Kingdoms levels.
Finally, there were goblins, who were escaped slaves of the fey who lived on a continent to the east. They have a lot of weird castes, from imps, who only halfway exist and only become material when in the presence of other goblins, to goblin pipers, who have terrifying magical powers and very little awareness of their surroundings, to Mabs, the goblin queens, who are basically kryptonians. They invaded from the east and formed a fourth faction.
Tolkien is a bit like this at time. Beleriand is elder days itself, so elves dominate and humans are vassals. Northern Third Age Middle-Earth is kind of dominated by hobbits (in the west) and dwarves (doing all the long distance trade); the human settlements of Esgaroth or the Wood-Men aren't exactly dominant.
Another twist is to have humans as the elder race, eclipsed by improved descendants like elves or dwarves. The Dragaera novels are on instance.
There are a few post-apocalypse settings that have much of humanity dying off combined with the return of elder races (+ magic). I can't think of one where any particular elder race is dominant, but they are all at least on par with each other and what remains of humanity.
I wish there was more experimentation with settings to shake up the Tolkien standard. I get that elves will always be popular in the this genre of fantasy as elves are to humans what Twighlight is to vampires and that humans will always will play a large role. Still it would be nice if more settings tried to shake things up by switching around who the big elder power is.
Dwarves: masters of artifice and the arcane who might have a bit of a problem with turning into dragons if they become too greedy and power hungry.
Gnomes: enlightened and inventive people from an Atlantis like civilization (maybe from the moon or farther out in space if you want to get really crazy) and are the main reason these "medieval" worlds are all over the place when it comes to technology.
Halflings: they just live quietly in that nice fertile valley that no one ever seems to bother. Well one warlord did try to invade it a few generations ago but had such disastrously bad luck that they never made it far past the border...