Can you purchase tickets in advance to visit Versailles, sort of like the museum tickets?

Yes.

look up Cartee Musee on the internet.1 day 18€, 3 day €,5day 54€. good for around 100 museums/sites in paris incl versailles (except gardens 3&euro

Sam

The easiest way to get advanced tickets for Versailles is to purchase them at the same time when you buy your RER train ticket at the station to go there. The advantage of getting there rather than as part of the museum pass is that the ticket you get at the station is good for both the gardens and the palace. My understanding is that you have to pay extra for the gardens with a museum pass.

PS: It's not worth it to buy a museum pass in advance of your trip to Paris, as they are readily/easily available throughout the city.