Drop Sink

Is it possible that my fall in the sink replaced by an undermount sink if I already have granite countertops?
I do not look down the drain with granite countertops, but it's too late to replace the battery with an undermount? Am I to get all the new outlets, it would be very expensive?
A Once you decide to fall in, its hard to turn color, due to cutting and polishing required around the hole. You may be able to find someone, or a representative can come and to estimate someone come in the fall to grind for in