Well, I bought an A300X DSLR from Sony and the camera itself has a built-in 2x teleconverter but the one I bought also comes with one, could I possibly make it 4x with the built-in one and the removable one without too much lose of quality?

well, if you have both go ahead and try it!

my guess would be that yes - it would degrade the image quality. How much? I couldn't tell you.

I'm going to try it, but I don't have the camera yet, I have to wait till around Tuesday before it arrives.