Hi there,

Does damage from consecutive acid attacks stack?

Understand that as a GM you could rule as you want but I am looking for the RAW interpretation of it.

/Pete

Define acid attacks, please.

It very much depends on the source of the acid damage. Two times Melf's Acid Arrow does not stack, because of the rule  of Combining Magical Effects in the Spellcasting Section of the PHB.

OK, as an example. First getting hit by a vial of acid, then another vial of acid, and finally an acid breath weapon.

That is not stacking. Each attack does direct and immediate damage of the given type (here Acid). So, each attack just does its acid damage independently of the other attacks that follow.

Stacking would be ongoing effects like the follow up damage from Melf's Acid Arrow.

And Melf’s Acid Arrow would stack with Tasha’s Caustic Brew. 

Edit: would the initial “immediate” damage from multiple Melf’s still land and only the lingering effects not stack?

Yes, as the rules for multiple spells of the same name state, the most powerful one of same spells will be applied. So, that means the first Acid Arrow applies its direct damage and its lingering effect. When the second Acid Arrow hits, the new Acid Arrow is the more powerful effect, because it has still its direct damage, so it does direct damage again, however, the ticking damage is only applied for the new Acid Arrow overwriting the first Arrow.