I bought a pizza stone without realizing that the max temperature it would withstand is 450 F (according to the instructions). My oven goes up to 550 F, which is the temperature I'd rather bake my pizzas at–is it OK to overheat the stone for the sake of the pizza?
As always, it comes to the meaning of "OK". The most likely scenario here is that the stone's life is shortened and it cracks. It's impossible to say when this will happen, it could be soon or it could stand up to hundreds of pizzas.
So if for you it is worth it risking the stone, you can do it. If you want to avoid with certainty the stone breaking after 4-5 uses, don't use it outside of the parameters determined by the manufacturer.
First disclaimers first, "always follow manufacturers' instructions." With that out of the way, the real answer is "it depends." If it has accessories (e.g. handles or feet), or is a composition stone (e.g. solid-surface countertop, which is made of mineral pieces plus bonding agents and filler - think of it like particle board, with a base material of stone rather than wood), then its maximum working temp COULD be limited by one of those other materials. (I have a formative memory of a spatula that melted when used in a hot pan. But I think that sort of inappropriate construction is less common nowadays, and unless your "stone" is made of plastic that doesn't apply.)
If it is a natural stone and nothing more, then it should easily survive whatever heat your oven can throw at it. Keep in mind that your "stone" was (we'll hope) designed for life inside your oven where, even if you baked at just 300 F, it will be exposed to MUCH higher transient temps. In a natural gas oven, for example, the flame will be in the neighborhood of 2,000 C. Granted, the burners will be behind baffles, but during heating there will be air currents that greatly exceed the set cooking temp, and any quality baking piece will have been designed to survive that incidental exposure.
Furthermore, mfr's recommendations (which you really should always take into consideration) can be somewhat arbitrary. There could be any number of legitimate reasons why they stamped it "450^F", but which don't actually mean it's no good at 550. I'm sure you're hoping for something definitive, but what I can offer is a high degree of confidence that unless you see some element that looks delicate and worries you, you can bake your pizzas and be fine. (In my experience your stone killer will be physical shock. I've always worried about thermal shock (i.e. placing a cold item on a hot stone), but I've yet to have a problem with it.