Rather than give the generic type1, type2 elemental damage where the only difference lies in its \"type,\" perhaps different elemental damage should each have its own special effect.
For example:
Cold damage: in addition to its damage, it can slow down monsters a bit.
Poison damage: The poison can be designed so that people would take advantage of its ability to do damage over a long duration. This permits someone who cannot tank well to hit and run instead.
Fire damage: no effects.
Lightning: has a small chance of stunning monster.