Short answer is NO. You are not supposed to shoot two guns of similar type one after another. You shouldn't shoot two center fires one after another, but you can do a center fire and a rimfire after each other, and you can shoot rimfire pistol and then a rimfire rifle one after another, but a lot of places discourage this and would prefer a break between people.
As per rule book, L 1 it is up to MD. L2 and up it is not allowed. 5.6.2, and 5.6.3