Assuming you can find a delivery place that offers vegan cheese substitutes or dairy-free flatbreads, is it safe to assume that the restaurant's dough recipe is vegan? What ingredients should you ask about?
Sadly a lot of the delivery chains add milk to their dough. Why is anybody's guess.
Dominos (at least in the UK...) offer a gluten free base which doesn't have milk but instead they add egg to it, those are the two ingredients you most need to watch out for. You can't usually ask these companies to leave ingredients out because they don't make the dough in-house.
Italian restaurants (the kind that make the base really thin and generally don't deliver anyway) tend to make the pizza dough in-house or at least using only the basic ingredients (flour, yeast, salt, sugar, water). But who wants to collect a pizza when they're being lazy and ordering pizza!
If you're not having a typical pizza base but some other kind of bread there's a risk of them using more 'premium' ingredients they can tout, such as honey or cheesy bread, or heck, bacon, anything goes at that point I suspect. But that's not very likely from a pizza delivery company.
If there's a Papa John's near you check their menu, where I am they have vegan pizzas, sides and dessert on their menu.