In my experience when it comes to table top RPGs we tend to get worlds and narratives in one of two flavors. Either there is one main thing going on in the world, and everything else is a side story at best. Or almost everything that comes up is capable of being it's own massive plot if the PCs decide they want to go that route. As with most things, people will vary between those extremes, but if I'm being honest I like the idea of their being a lot of big stories in a world even if the campaign is only focused on one. It gives a sense of a world in motion where things are happening outside of the PCs' journey, even if all we get are glimpses of those stories.
In general, the PCs should come across big stories and small stories as they move through the world. They may be pursuing the vein of one narrative, and then perhaps change tracks to a different one if it grabs their interest. THis doesn't mean the other stories go away - remember them and who was involved - but if things draw the PC's attention away they shouldn't feel trapped to not go that way. At least, unless of course they've driven situations to where ignoring it is like pouring gasoline on a gas stove, turning it on, and walking out of the house. Actions do have consequences after all.
Even with that, I don't think you should stop spinning stories just because one story is big, the focus, or dire. Other things are going on in the world, and those things will cross the PCs' path. Indulge it. Flesh it out enough the PCs can see what is happening, and if they jump tracks let them. The other train keeps going, just now without anything trying to guide it. But as long as people are having fun the game is going well. And when those consequences do rear up, they don't have to be all bad.
You can't have a living world that feels 'real' where what the PCs choose to do matters if everything just stops as soon as the PCs aren't looking at it. So make those stories meet at crossroads, and see which one takes the focus. Remember, there's no such thing as a "side quest" in a table top RPG - not in the sense of a computer game anyhow. All we have is what story is taking the focus of this session, or perhaps the next few sessions in the game before we move on to the next tale.