Private high school(s)

(1a) Jordan has many years of experience tutoring students who attend private high school.

(1b) Jordan has many years of experience tutoring students who attend private high schools.

My non-native English speaking friends think both "private high school" and "private high schools"

work. This is their reason. "Private high school" refers to the level of education as in elementary school, high school and college, so the singular form of "school" carries that meaning. On the other hand, the plural form of "school" focuses on the learning institution itself that offers different types of courses at the specified level.

I think my friends' explanation makes sense to me. What is your opinion? Many thanks.