Specifically relating to enchanted/cursed/legendary items - as we can use any gem in those. From my quick tests:
- at least according to flying damage numbers (you can enable those in options) multiple-elements is not possible, excluding physical damage (although in context of white items, you cannot put e.g. fire and phy gem on the same item)
- same type of damage does stack though, as do stats like armor
Heres some of my notes i had not sure if still relevent or what patch it was on fyi.
You can stack any of same element.
Gem+element infusion. (A second gem on enchant item is either so miniscule it doesnt add or i had bad rolls and didmt hit the next dmg)
You can add a second element gem to enchant item. However it does not combine. Fire enchant with plague gem you only get one (i domt remeber which, i put it in a post somewhere when i experimemted it)
However it will boost damage from a skill that uses that element.
Examlple you have plague and fire bonus your weapon is dealing fire dmg, when you plague throw, this is boosted. Niche but its there.
You cannot mix gems on white gear that have similar skills. If its focus gen you cant add focus% as well. Same with dmg types.
Random note elemental infusion is 100% elemental damage and 30% damage boost so if you mix physical with an element (can mix) on a weapon you will lose your x% physical bonus on the normal attacks which typically split thks damage. Runes like fire throw are 100% fire btw.