The name of the romance novel at the start of the movie which Chris (Phoebe Cates) narrates to her roommate Betsy (Kathleen Wilhoite) was "Storms of Passion". The book appears to be fictitious as there is no author listed on the cover and an internet search for that title comes up empty.
The scene where the Rolls Royce drove into the pool (see filming locations) was filmed only two miles from where The Dirty Sanchez (which is actually called The Garage Motor Club) was filmed in Dodgeball: A True Underdog Story (2004).
Phoebe Cates got cast in the top-billed role in this movie after her successful appearance in another youth movie, Fast Times at Ridgemont High (1982), which had been made and distributed by the same Universal Pictures studio the previous year in 1982.
According to the 80s Rewind website, Sylvia Kristel appeared in Private School "only as a contractual obligation to the producers of this movie. She had previously worked with them in another "Private" movie . . . Private Lessons (1981)".
Publicity for Private School (1983) did sometimes, rightly or wrongly, report that it was a sequel to Private Lessons (1981). Both movies had title similarity, the presence of actress Sylvia Kristel, the same producer R. Ben Efraim, and American video distribution through MCA/Universal.