There is no problem if a singular subject is having one or more objects.
singular-singular:
The student sat down on his seat.
singular-plural:
The student looked at his books.
There is also no problem with multiple subjects having multiple objects.
plural-plural:
The students had to compile a list of their books.
But what is the proper construct in the plural-singular case?
Variant 1:
The students opened their book.
Variant 2:
The students opened their books.
(In case we are trying to describe that each student opened exactly one of their books.)