I mean I'm careful to only order from the place down the road that does a BOGOF offer. I'll eat one there and then and let the other... stink out the fridge unless the family gobbles it up the following morning.
That's fine. The main loss at this point is texture/dryness. I like to fry old pizza in olive oil in a skillet, then lid with the heat off for a minute. The steam melts the cheese and it comes back to life.
As long as it doesn't have sea food or chicken I'd expect it to be fine for a week in the fridge. Ideally, you put some kind of cover on it to protect it from spores.
I guess it also depends on the toppings. Like, seafood and big chunks of vegetables spoil faster than, say, cinnamon sticks (but the latter is quite a rare sight on pizza). At least if you care more about the food safety aspect.
Otherwise, if you were just looking for various opinions (or preferably, equivocal ones), I personally wouldn't eat it later than the second breakfast time. I mean, the breakfast two days from delivery, not the hobbit meal. Also, if it's as late as the 2nd day, I wouldn't do that on a work day, or if I'm not guaranteed to have a safe emergency toilet opportunity.