On a superliner car train with the material handling car on the rear do private cars go behind that car?
Depends.
I was on a trip from washington DC to Chicago where two private cars were being dropped at Cincinnati. No switcher on duty.
The cars were cut off and the remainder of the train continued to Chicago.
Of course in recent years, since 2003, you won’t find any MHCs in use.
Good Luck, Ed