Let's say you are a human warlock with the Mask of Many Faces invocation. You cast disguise self and alter your form to that of an elf. While under the effect of this first illusion (before it expires), you cast it again to change your form to a dragonborn. What happens?
Do you go from elf > dragonborn? Do you temporarily revert to your base human form?
The rules for Combining Magical Effects (PHB pg 205) come into play here:
The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.
For example, if two clerics cast bless on the same target, that character gains the spell's benefit only once; he or she doesn't get to roll two bonus dice.
So what is important here is to determine which effect is the most “potent”.
There is no clear guidance in the rules on how to determine potency when two spells have the same effect. There are some reasonable options in this case:
My ruling from the games I DM is that the players can choose when they cast the second spell if they want to use either #1 or #2, but only if they are casting it on an ally. If they are casting the spell on an enemy I apply #2.
In your case these two options are functionally equivalent, so you would look like an Elf that turned into a Dragonborn.
As has been stated elsewhere, there would be no "overlapping" effects from the two castings of this spell.
'The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies[...].' (PHB p. 205)
This has been further clarified by Jeremy Crawford on Twitter (emphasis added):
The effects of the same spell don't stack; use the most potent effect (PH, 205). If equal, use the most recent.
Both castings of this spell were definitely equally potent (they required no spell slots, and were cast by the same magic user). So only the most recent one would apply. Now let's consider whether there was ever a period when you appeared human.
Spells (or their effects) end only when conditions are met which end them. The only thing which made the effect of the first spell (Elf disguise) end was the effect of the more recent casting of the same spell (Dragonborn disguise). So there was no time when neither spell was in effect, so you never looked like your base human form.
Of course, if someone saw you casting the spell (which has verbal and somatic components) and changing into a Dragonborn, they would likely come to the conclusion that your appearance was a the result of a spell. But they would never have seen your true form.
If you dismiss your first casting before casting the spell a second time, then your normal form would be visible. Both dismissing and casting Disguise Self requires an Action and you cannot use two Actions simultaneously. Even when a feature allows you to take two Actions in a combat round, the actions are still understood to occur consecutively, not concurrently.
If you dismiss the first Disguise before Casting a second Disguise Self spell then they aren't concurrent spells.
While it might be amusing to think about the intangible hat you can create with disguise self, it isn't simply a magical hologram. If Disguise Self worked like a hologram then it would be impossible to disguise yourself as someone shorter or thinner than your original form - your head or your stomach would end up poking through the disguise.
'The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect—such as the highest bonus—from those castings applies[...].' (PHB p. 205)
So, while it might be funny to imagine two overlapping holograms, a shorter stockier dragonborn, with an elf's head sitting on top, delicate fingers semmingly extending from the dragonborn's finger tips, magic disguises don't work like holograms. While both spells are active, one would simply take precedence over the other.
Let's refer back to that rule again...:
'the most potent effect—such as the highest bonus—from those castings applies while their durations overlap.' (PHB p. 205)
Diguise Self requires an Intelligence (Investigation) Check against spell save save DC, from a creature that wishes to work out whether or not you are disguised.
If two different casters had cast Disguise Self on the same target, it seems logical that the spell cast by the one with the higher spell save DC would be considered more potent and take precedence, until it was dismissed or its duration expired.
However, when the spell save DC is the same, either between two different casters, or because the same caster has cast Disguise Self twice, there is no guidance as to how 'the most potent' spell should be adjudicated.
A DM should choose a method, make sure the players understand it, and then ensure they apply it consistently.
I personally would rule that the most recent spell cast takes precedence, effectively overlaying the previous casting.
For evidence of a similar (but not definitive) ruling, that some might choose to consider authoratative, you might be interested in this tweet from Mike Mearls:
Q: Could you use multiple castings of Disguise Self to layer a disguise and force multiple checks against DC?
A: No, I'd only apply most recent casting.
See also, this tweet from Jeremy Crawford, which agrees with this general principle but isn't specific to Disguise Self.
If the second spell is ruled by the DM as more potent, then the PC will change into a dragonborn as soon as the second spell is cast. This is what I would rule happens.
If the DM rules that the first spell is 'more potent', the PC would only appear to change from an Elf into a Dragonborn when the first spell's duration expires.
It states on page 234 of the Player's Handbook,
You make yourself-including your clothing, armor, weapons, and other belongings on your person-look different until the spell ends or until you use your action to dismiss it. You can seem 1 foot shorter or taller and can appear thin, fat, or in between. You can't change your body type, so you must adopt a form that has the same basic arrangement of limbs. Otherwise, the extent of the illusion is up to you.
But then on page 205 it says that spells don't overlap and that the player keeps the most potent of the two spells that is cast on it.
So that means the first disguise self spell that was in affect on you would end if you recast disguise self to make yourself like a dragonborn.
