You can't take moves from another playbook if they don't make sense.
A lot of moves refer to things specific to their playbook - Legacy moves talking about members of the legacy, Janus moves talking about their secret identity; heck, even Outsider moves talking about their homeworld, though that's more a backstory than an extra.
Getting a move from another playbook means that you're acquiring those abilities in the fiction, not just on your character sheet, and nothing happens unless it makes sense in the fiction. So, for any of those dependent moves, the GM and players are going to need to work on making them make sense in the fiction.
If you already have a Protege, or a Legacy, or a Janus, well, it's not unheard of for a mentor or a legacy or a secret identity to draw another hero into it. Secretly or unknowingly being from space isn't outside the realm of comic-book possibility, either. But ultimately if the GM can't find a way for a move to make sense for a character to take from another playbook, they can't take it.
So let's work out your example case: someone else taking the Protege's Venting Frustration. Dusk has been reaching out to Mentalla a lot lately - she's an established hero with mental powers, and while she can't absolutely relate to Dusk's edge-of-oblivion mind vision she does help Dusk adapt to a life where they have it. When Dusk gets an advance they decide to take a Protege move and it's at this point that they talk over with the GM about whether Mentalla is going to be a mentor and what kind of labels she embodies and denies. (Not that it matters, but Mentalla believes in responsibility through self-control, embodies Superior, denies Freak.) The first move Dusk takes from Protege reflects the, uh, rather rocky start to this relationship.
But in addition to this, Mentalla is now Dusk's mentor, and will involve herself in Dusk's life and heroics in ways another adult would not, even if Dusk rejects her influence - the GM should probably start looking at the Protege-specific GM moves in addition to the Doomed moves when thinking about how Dusk's life gets complicated.