What's the approximate extra cost to building a basement under a three car garage? I realize additional support is needed, but other than that, I'm not sure what extra work is needed and what costs are associated with it. Since there's a slight slope to the property I was hoping to be able to have a direct walk out basement with the exit being under the garage. But after some calculations, I realize that a full basement under the 1st floor (no garage included) will give another 1,500-2000k sq footage to the house. (I plan on putting in the frame, electrical and plumbing and then finishing the basement later to save on cost). But if I build a true full basement, utilizing the space under the garage, that will give another ~800 sq feet (potential apartment for extra income in the future).

If I find that I can afford the extra costs associated with expanding the basement to under the garage, there's a possibility that a bedroom would be under the garage as well. What are the pros/cons of this? What extra insulation (or other things) are needed to make sure that this is a safe area? (Fumes are my biggest concern).

Thanks!