The assembly line approach to making multiple pizzas: Lightly brush one side of a dough round with olive oil and place it oil-side down on the grate directly over the coals. Replace the grill cover and oil the next round.
After about 1 minute, open the grill. The first round should look puffy and have clear grill marks on the underside. Remove it and flip it grilled-side up onto a cookie sheet. Quickly spread it with toppings, then return it to the portion of the grate that's over indirect heat. Place the next oiled round on the grate over the coals. Replace the grill cover.
After another minute or so, open the grill to check on the untopped pizza. If it's ready, remove it, replace grill cover, then add pizza toppings. The pizza in the grill should be done by now; if it is, remove it to a cutting board and place the newly topped pizza over that section of indirect heat. Place another oiled round over the coals, maintaining this system of topping and shifting until all the pizzas are baked.