You can build a drone, any size/feature/number of motors (from 3 to 8, usually). It would not be a Phantom, though, since most of the Phantom components (like the flight controller and gimbal) are proprietary and not likely to work when installed in different size drones. You could move your P3S components to different frame, but would need to keep (roughly) the same distance motor to motor and roughly the same weight and weight distribution (i.e. would basically end up with a very similar drone). The P3S firmware is optimized for a drone that looks like a P3S, and won't work well outside of that. Generic flight controllers allow you to change its parameters for any size drone (any weight, number of motors, etc) but require some understanding of PID tuning
) when building a drone was the way to go: more features, cheaper. These days if you need a generic drone for video applications, a P3S competitor is impossible to build DIY for less/same features (i.e. you can either build something for less, but will have fewer features, or something better than a P3S but for much, much more). Vertical integration and mass production has dramatically lowered prices (in no small part because DJI wants to maintain their market presence by pricing pretty aggressively).
