a person with black hair, I would have to say dark reds like auburn, burgundy, and other dark red colors are popular choices and they will not clash with a business persona, however if you want to get a snazzy new look for a younger and more hip person, you may try highlighting with very dark purples and very dark blues, these give you a cool flare and dependant on how dark they are will be very mild in your hair and can be As hidden with up-swept hairdoes.
