When using base/clear combos to paint cars, which is pretty much the only way they go these days, the base coat lays flat, no real gloss. The shine comes completely from the clearcoat. Even if you buff out the basecoat, you'll never be able to get it look like the rest of the car. It's nothing like the single stage paints like urethanes or enamels where you lay the paint down and buff the shine up.
Also, especially factory paint jobs, the amount of basecoat is as minimal as they can get away with. If you attempt to do what you are thinking to do, there is a real probability that you will sand and/or buff the paint right off of the car.
Unfortunately, the only real way to rectify the issue is to repaint the car.
We own two. Don't you??