For booming blade, the 'spell effect' is that the target is sheathed in a sonic bubble. That bubble has certain qualities regarding what happens if you willing move through the bubble, and ALL of those qualities ARE the 'spell effect', including what happens in the world to cause the bubble to burst (trigger) and the consequence of the bubble bursting (thunder damage, spell ends early).
Since the sonic bubble (and its qualities) ARE the 'spell effect', then you cannot have two of them on you at the same time re: Combining Magical Effects. Since you only have one bubble even if two spells are on you, there is no trigger for the second bubble to burst because there is no second bubble to burst!
However, when the first spell ends (for whatever reason) then there is no longer anything preventing the second spell from applying, and so as soon as the first bubble goes away then the second spell forms a new bubble, and the qualities of that new bubble become relevant.
Assuming this is all true, and IMO it's a completely valid interpretation of the rules, the challenge I can see with this is now in interpretation.
OK: Character sheathed in two or more Booms. First BOOM goes off. Second one is now ready to come on-line. What exactly happens?
1) SLIGHT DELAY: They moved, triggering the first one, and complete 5' of movement - the smallest intentional move increment in 5E - as the second sheath comes online. That's because the intent of the spell is to prevent them from disengaging, and they actually have to disengage to trigger it. So, they've moved 5', are no longer in melee range unless you close again, wrapped in the second sheath - and they have the choice to stop, or keep moving to trigger the second one. So,
actually moving is key.
2) QUICKLY: It comes online almost immediately, so the character moved 1' at most - negligible - and are considered to be in the same square, and the character is aware of this and stops moving before the second one goes off. This is because the character
choosing to move is the key.
3) INSTANTLY: The character starts moving, and the second sheath comes online instantaneously (there's no delay built in to the rules), so there's no reason to give a character the potential to stop moving. So, the character starts moving, and they happen one after another immediately, like a zipper made of those 'pulling string' fireworks. BOOM BOOM BOOM. Sucks to be you, character.
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With your reading, all three of these are possible because of the weird nature of Booming Blade - it has a duration like a status effect, but it does damage, triggered by movement.
I can see #3 happening to an unintelligent foe quite often. Constructs, animals, stuff like that.
I'm kind of stuck here, because I'm sensitive to the kind of 'combinatorial cheese' that 3X had, where taking abilities that were meant to shore up the weakness of one class into another creates some crazy combos. So, maybe someone else can tell me - stacking BB effects that can all still go off one after another - how abusable is this?