It depends on how much more..
once you fill it more than capacity, you'll start to choke the engine, get worse gas mileage and performance, etc.
One time I filled my car a little too much (previous) and then took it in for a 60K service, telling them not to change the oil. They did everything and added BGMOA after I said not to do anything w/that. My car was filled 3/4 a quart more than it should. I felt a loss in acceleration, gas mileage went way down (that's b/c too much oil is getting sloshed around by the cam shafts I think). I drained a little out and she perked up.