I have waxed over other wax before with no ill effects. You should wash it right before you wax it so there is no dirt on the paint to rub into the clearcoat when you are waxing it. Even a little dirt will act like sand paper and you'll see little scratches, or swirls in the paint. Not sure what color your car is, but the darker colors show those swirls a lot more than light. Since you have to wash it before you wax, you may as well use the dawn to clean the surface of any other sticky substances, along with old wax.
Good luck!