You don't change class when you become educated. You may change income brackets though. College education can turn you into a lawyer or into a doctor, but it is very unlikely to turn you into the inheritor of a multi-million company.
This got me thinking what exactly makes someone a member of the ownership class. I'd agree inheriting a multi-million company would make you a member, but does owning a small business with a few employees? How does debt factor into this? A business owner who's trying to pay down their startup loans might feel more like working class than ownership.
Who is the ownership class?