If everyone agrees, you can do the whole process a second time, but if 1 person says 'no,' you don't. Then you do the same with the person across from you (second pass) and then for the person to your left (third pass). All you do is take 3 tiles from your hand that you want to discard and pass them to the right, called the first pass.
You must do the Charleston the first time. This rule is a variant, and it's typically only used in the American version. Pass tiles using the 'Charleston' rule in American mahjong.