Suppose I have a ranger with the style Archery, and I take a one level dip into fighter and also pick Archery. Do I get an additional +4 to my attack rolls, or just +2? More generally, does the same Fighting Style stack with itself in other cases, like dueling with Paladin and dueling with Fighter?
Everywhere that you can get a Fighting Style includes this important sentence:
You can’t take a Fighting Style option more than once, even if you later get to choose again.
So it doesn't matter whether it stacks with itself, because you can never take it twice.