It depends what you mean by private schools. For the Generations EP boarding schools, no or at least not that I know of. But NRaas StoryProgression can be used to give an otherwise public school the private designation so that, for example, tuition fees are set, a uniform is required, and registrations can be restricted
(SP Career add-on module required for some of these options). But that doesn't make the school behave like the mod's specialty schools that convene at other career rabbitholes around town, it just makes what was a regular school into a private one.