The CoE campground I use allows one RV plus one tent or shelter, or two tents in each designated campsite; there is also a two vehicle maximum. In the tent camping areas, the rule is one tent per camping permit. We have similar rules in our state parks, but it varies. Some have separate tent camping areas, and some designated sites are RV only or tent only, and the tent has to go on the RV pad.
Many of the commercial campgrounds I've used do not allow mixing tent, cabin, and RV uses, these are separate areas of the campground. Most of the RV resorts I've been in do not permit tent camping, and not all allow erection of a screen room or shelter.