Vanity Outlet How Do I Add An Overflow Outlet To A Bathroom Sink?

How do I add an overflow outlet to a bathroom sink? - vanity outlet

Recently, I renewed my bathroom upstairs and used a top vanity sink with pre-registered. The sink has an overflow hole, but I never thought that a problem until my friend, the water runs down the creek left available!

What I know is that if it is possible to do something like a hole in the sink, and somehow add an outlet to plug leaks. Is this reasonable or should I try something else? Any help would be appreciated.