Let O and F be an operation and a language family, respectively. So far, in terms of closure properties, the classical language theory has only investigated whether O(F) ⊆ F, where O(F) is the family resulting from O applied to all members of F. If O(F) ⊆ F, F is closed under O; otherwise, it is not. This paper proposes a finer and wider approach to this investigation. Indeed, it studies almost all possible set-based relations between F and O(F), including O(F) = ∅; F 6⊂ O(F), O(F) 6⊂ F, F∩O(F) 6= ∅; F∩O(F) = ∅, O(F) 6= ∅; O(F) = F; and F ⊂ O(F). Many operations are studied in this way. A sketch of application perspectives and open problems closes the paper.