The reason I suggested looking at Section 503.1.4, is that you have a 4-story building but plan on putting a Group A on an occupied roof--you may not need to go to Type IB construction. Exactly the pickle I'm in. Met with the B.O. to discuss options and what he was comfortable with. We're looking at either <750 SF of enclosed roof deck (Type II-A, 5 stories, all B use) vs. >750 SF (Type I-B, 5 stories, with A3/B use). To get down to II-B, 4 stories, I can only pop up the elevator and have no enclosed or covered space on the roof level.
Per Table 504.4, a Type IB building allows a Group A to be on the 11th story for nonsprinklered ("NS") buildings and on the 12th story for sprinklered ("S") buildings. However, Type IIA construction allows a Group A to be on the 3rd story for "NS" buildings and on the 4th story for "S" buildings.
Assuming your building is sprinklered throughout yep and you're not using the sprinkler for an area increase (it's a California thing), nope then you can use Type IIA construction because Section 503.1.4 states if the occupancy group is permitted on the story below the occupied roof, then you can have that occupancy group on the occupied roof. Thus, you don't need Type IB construction to allow a Group A on the "fifth floor." B.O. disagrees. He says anything over 750 SF on the roof = 5 stories and an A3 use = I-B.
If you're using the sprinkler for an area increase, then Type IB construction is what you'll need. for a 4-story building that won't affect enclosed stairways and elevator hoistways. However, all penetrations in horizontal assemblies (except the roof) will need to be 2-hour assemblies. One of the benefits of going to Type IB construction is that the walls for shafts (stairways, elevator hoistways, chases, etc.) can be supported by the floors since they have a fire-resistance rating equal to the shaft enclosures.