I'm not sure I understand what you're asking. Bosses already randomly target other players avoidable attacks, they just don't suddenly drop aggro. There's also already many mechanics that tanks must deal with protect the party, like the tank towers in EX1 or grabbing tethers in EX2.

There are bosses that ignore the tank and just attack random players, but they aren't all that threatening, especially for tanks since the damage has to be low enough that it doesn't 1-shot other roles. Using 4 tanks against Rathalos Extreme was very common back in the day because of this.

What would the mini-game to stop the boss from "raging" be? Provoke it? Stun it? An Active Time Maneuver? Could use an example.