I am not sure under what LEED certification type this building would fit better...

The building is a higher education student center that will have only the exterior walls and HVAC systems renovated/replaced. The idea is to keep the building operational while the renovation is happening (thus it should not fall under NC/Major Renovation).

Can this be certified under C&S? As this is an existing building, obviously the interior is already designed, but it will not be part of the scope of the project and no/very minimal changes will be made to the actual interior of the building.