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Some combination of Demoted to Dragon and/or Make Way for the New Villains depending on how the new villain handles their new underlings- say, do they take over the organization as-is or kill half of them and demote the survivors to "guy who brings me coffee". Note that the Nebulous Evil Organisation as a whole might be the entity being "killed off" or demoted from Big Bad to The Dragon. (Say, the leadership being usurped was a shadowy council known as The Cabal rather than an individual leader, and the members now serve as a particularly large group of Co-Dragons)
Evil Is Not a Toy if the newcomer is something along the lines of Sealed Evil in a Can (this can get abstract/metaphorical- say, The Cabal broke a Psycho for Hire out of prison to kill the heroes and this ends up happening)
Edited by Scorpion451
A powerful established group cooperates with a newcomer and believe she/he will be their front figure, but they can control her/him. As it turns out, they were completely wrong and are now the conttolled ones.