Argent Peacemaker and Sentenza used to have split damage types and for some reason that was taboo. Here's why, statistically, dual-special damage is doable:
Piercing/Shadow
Strong: Gremlins, Beasts
Neutral: Fiends, Jellies
Weak:Constructs, Undead
Piercing/Elemental
Strong: Undead, Fiends
Neutral: Constructs, Beasts
Weak: Jellies, Gremlins
Elemental/Shadow
Strong: Jellies, Constructs
Neutral: Gremlins, Undead
Weak: Beasts, Fiends
Two super-effectives, two neutrals, two ineffectives, just like with pure special damage.
That's not how damage works.