There are ways to get a ton of followers at once, but they take time to set up, and/or need certain parameters. At a certain part in the story, you can have 3 legit followers, a dog, a horse, and still be able to resurrect dead bodies.
Other than that though, you have to go up the Conjuration tree and unlock the perk to have 2 summons at once. If you do this, and also have the Undead thrall spell, you can ultimately have two undead followers who are immortal. This is on top of having a dog or other “pet”, as well as a horse.