A "unicorn" is the bisexual woman an established couple goes looking for so she'll date both of them on the couple's terms, and "unicorn hunting" is that search — named for how rarely anyone actually agrees to it.
Picture the brief: a couple, usually straight-leaning, wants a third. She should be a bi woman who dates both of them, dates nobody else, doesn't rock the balance the two of them already built, and — bonus points — eventually moves in. It's a package deal with the terms written in advance. The word "unicorn" is the joke and the diagnosis at once: someone who signs up for exactly that is about as common as a mythical horse, while the couples drawing up the brief are everywhere.
That's why the non-monogamy scene tends to side-eye the whole move. The problem isn't three people wanting each other — it's the wiring. The couple stays a unit with a veto and a shared exit; the third arrives with a role, a rulebook she never got to negotiate, and no matching power. She's cast as a fantasy accessory rather than a person with her own desires, her own other people, her own reasons to walk. That imbalance is the line between "unicorn hunting" and an actual triad, where three people build something as equals instead of installing a plus-one.
Here's the reframe worth keeping. Wanting more than two in a room is not the crime. Treating a human like a feature you bolt onto your relationship is. If you genuinely want her — her agency, her other connections, terms you all write together instead of a contract handed over at the door — congratulations, you're not hunting anything. You're just dating. Do that instead.