In remodeling, cantivered floors are somewhat more expensive and diificult to construct but are rarely out of the question. The biggest constraint is that the cantilever can only extend a limited distance, usually around 24 inches, without very specialized structural support. Cantilevered floors usually require joists extending back into the existing floor a distance equal to or greater than the cantilever. The cantilever may also affect the roof if it extends beyond the eave line. Also, be sure that property lines or building setback lines are not violated. I recommend that you engage a qualified contractor or architect for design advice and design.