I'm getting the impression that you're not looking for a story, so much as a world, a framework in which stories can take place. Consider, then: what is that world like? Our world (more or less)? Our world + supernatural stuff? Futuristic? Past? Fantasy world with fantasy races?
Once you have the general setting, who are the relevant active parties? Are there any opposing factions? (Consider how Assassin's Creed have the recurring Assassins vs. Templars enmity throughout the series. World of Warcraft had the Alliance and the Horde - two opposing factions, each consisting of several subgroups.) Who are the important figures within each active party?
What role does the player-character play in the world? What kind of impact is he meant to have?
Once you've established the world and the player's place in it, you can treat quests as stories (big stories, small stories) told in that world.
You want your players to feel progress. That means that the player's actions should have an effect on the world, that the world should be changing as the game progresses. (In MMORPGs, changes would be effected not by one player, but through the collaborative effort of many players.) One way to achieve that is to have an overarching story. For example, in Ni No Kuni II, the overarching story has a deposed child king trying to create world peace. As you progress through the story, there are multiple small quests (help a woman entertain a sick child, find a girl's lost pet) - those give you small bonuses, like NPCs joining your cause. There are bigger quests (find out what's corrupting a city) - those have world-changing effect that progresses the main story, and change the world in which you're playing. And then, the game itself is a part of a franchise - the effect of what you did in the first game is visible in the second.
You will be able to find more relevant information under worldbuilding.