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I've seen many posts and discussions online that assume that the damage-over-time spell effects such as Melf's acid arrow (Player's Handbook) and vitriolic blast (Compete Arcane) self-stack, meaning that hitting a target with a second spell will deal additional damage each round. One warlock eldritch essence invocation, brimstone blast (CA), even has (poorly written) language presumably to specifically exclude itself from this capability.
However, stacking DoT spells might fly in the face of the rules for combining magical effects, specifically these two sections:
Same Effect More than Once in Different Strengths In cases when two or more identical spells are operating in the same area or on the same target, but at different strengths, only the best one applies.
Same Effect with Differing Results The same spell can sometimes produce varying effects if applied to the same recipient more than once. Usually the last spell in the series trumps the others. None of the previous spells are actually removed or dispelled, but their effects become irrelevant while the final spell in the series lasts.
This section would support that damage effects stack, since damage is not named as a special case (only bonuses/penalties):
From Player's Handbook page 171:
Spells or magical effects usually work as described, no matter how many other spells or magical effects happen to be operating in the same area or on the same recipient. Except in special cases, a spell does not affect the way another spell operates.
There is no mention of restrictions to damage -- all examples given for the section in the PHB relate to buffs and penalties except for the section regarding Instantaneous Effects:
Two or more spells with instantaneous durations work cumulatively when they affect the same target. For example, when two fireballs strike a same creature, the target must attempt a saving throw against each fireball and takes damage from each according to the saving throws’ results. If a creature receives two cure light wounds spells in a single round, both work normally.
This could be interpreted as saying that in all other cases, damage does not stack. However, the rest of the section deals with bonuses and penalties rather than damage, so fireball could just as easily have been a poor choice of example.
Here are some posts on other message boards implying that the damage effect from Melf's acid arrow and vitriolic blast are supposed to stack:
Multiple instances of Vitriolic Blast stack, so if you attack thrice with Eldritch Glaive, you'll do an extra 6d6 damage on the next round, and so on.
Vitriolic Blast seems to be a "must have" invocation to me. I haven't ever heard of a warlock that didn't get it or doesn't plan on getting it. It makes sense, being the only way a warlock can ignore SR and hurt golems. The automatic (no save), stacking extra 2d6 per round is pretty impressive as well. [emphasis added]
What stacking rules? This is no bonus or malus, it's simply damage.
The consensus from what I can find online seems to be that damage is not considered a bonus or penalty, and thus is not part of the stacking rules. However, the game seems to be unclear from what I can tell. All examples given for "can't do" are definitely not damage examples.
So the big question is: Do damage effects on a specific target stack?
This post is different from a related post because it deals strictly with damage stacking and not bonus/penalty stacking. Damage stacking appears to possibly be a special or at least different case.