Most conserved quantum numbers are additive in this sense; the electric charge is one example.
Any conserved quantum number is a symmetry of the Hamiltonian of the system (see Noether's theorem).
Thus, all symmetries which are mathematically similar to parity (physics) give rise to multiplicative quantum numbers.
In principle, multiplicative quantum numbers can be defined for any abelian group.
An example would be to trade the electric charge, Q, (related to the abelian group U(1) of electromagnetism), for the new quantum number exp(2iπ Q).