Do different types of elemental damage stack?
I'll keep it short: could I combine the effects of, say, a bomb that lights enemies on fire and a bomb that causes stun so that I can keep my enemies from attacking AND keep them on fire all at once?

Keep in mind, certain status effects can cancel each other. (I've only noticed this with fire and ice. Actually this is a good thing as they'll constantly be lit on fire and frozen in bomb vapour fields and enemies get hurt everytime they're lit so....)
what about the dmg types from silversix? elemental and piercing do they stack? and if one is resisted are both? it seems like 90% of mobs are resistant to piercing.
Weaknesses will proc despite the secondary type's resist, but the resist still overpowers into saying it's ineffective. You'll do more damage to Construct mobs with a Silversix than you will to a slime despite them both having piercing resistances.
You can combine status effects, but all elemental damage is basically the same.
For example, all the alchimer types do the same damage as they have the same amount of elemental damage.