I was going to say no, with Mind Daggers, Fireballs, etc. The damage duration is usually considered an instant effect, it is only the Partial Blindness and the Defense Penalties that have a multi-round duration, thus the damages stack, but the penalties do not.
But then I remembered that the rules list no "Instant" duration effects. Every spell says it lasts at least one round. Thus an argument could be made that since all spells last until at least the end of the round they were cast, and since spells don't stack, the rules as written could be interpreted that only the "biggest" instance of each spell can affect any one person. Only the biggest fireball and/or the most damaging Mind Dagger do damage, with the lessor successful castings of duplicate spells that strike the same target being discarded.
Bare in mind that I know of nobody who has ever even considered playing that way, but now that you point it out, the way it is written could support that interpretation. But I am pretty sure that most people play that damage stacks and it is only penalties and bonuses that don't stack.