If you grow your writing from short-stories, to longer stories and novels you will have to create more content. Most of it will be more detailed description of settings, people and plot. Also you will add more obstacles to create a longer main-story. But another possibility is to add side-stories. That can be somewhat difficult, as too much side-story might be distracting, the reader not longer knows whats the writing is about. Are there any rules of thumb, how much side-story is acceptable?
I'm not sure there is a hard and fast number, but there are other ways you can measure if the side story is acceptable. What does having it in your story achieve. If it's just there to fill out the word count is it worth having it there at all?
On the other hand, if the story story helps move the plot along or helps develop the characters it might be worth having in the story. Sometimes major characters can't be there for all the important events, so having a secondary set to see what's going on can help flesh out the world and increase the tension. It also lets you break up the flow of the main story to help with the placing. And there's always the option of ending a chapter on a cliff hanger then jumping to the side story for a chapter or two.
If you're doing a world spanning epic it might make sense to have dozens of side stories. If you're doing a small story that never leaves the local neighborhood you might only have one or two, or none at all. It really all depends on how much the help the story.
Sometimes side stories are useful to show how bad things are going. Disaster stories and war stories both do this. It allows you to show how bad things are, and if done right you can kill off one of this minor characters after building them up enough that reader will feel the loss.
There is no answer. "3" (if you can actually count them) side-stories can be too much. Even 1 can... if you want to write (or rather, if the story demands to be) a simple story.
3 can be too many. But 100 can be just right. It depends.
Haven't read the Wheel of Time yet, but I've heard it contains lots of side-stories. Too many? Some surely think so, but then they're not the audience for it. Given it is a success, it looks like it didn't contain too many tangents.
So... as I always say: write your story the way it demands. If it's an intricate, multi-level plot, then there will automatically be "side"-stories (some of them, or even most of them, won't really be tangents, it just won't be obvious how they're all connected for some time, see "Pulp Fiction" for a great (non-linear, too) example)