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Keegan was weak-willed compared to you who managed to resist Alma several times (B button sequences) so Alma uses Keegan to lure you to the Amplifier, despite your intentions to go there regardless. While you're strapped into the chair, she rapes you and you supply her with a third child, a child that Armacham will not take away from her, a child for her to finally keep. Keegan, not understanding why Alma used you to produce a child and not him, has a battle of psychosis with you (this plays out as a gunfight). If you've collected the intel about the Harbinger squad-members, you'd see that Becket's telepathic levels are listed as Very-High while Keegan is only listed as High. Keegan's mind was weaker, and Becket's was stronger. Becket wins the fight and Alma chooses him for being a more able telepath and more strongly willed compared to Keegan. While you're fighting Keegan, you're using your psychic abilities to telekinetically press the switches to the Amplifier that open it and extend the bridge, the switches you pressed earlier.

Snakefist wanted Becket to jump into the Amplifier and lure Alma there. He would then turn on the Amplifier so you would be strong enough to defeat Alma in a battle of psychosis. This obviously doesn't happen.

Aristide wants Becket to get into the Amplifier and lure Alma aswell. She'd then close the Amplifier and use it's suppressing field to keep Alma inside. With Alma alive and imprisoned, she'd be able to bargain for her life against the Board of Directors (the people who run Armacham) who had sent their personal army to kill her (ATC). This doesn't happen either as Alma sends Aristide flying across the room into the wall, presumably knocking her unconscious. With Stokes dead, and Aristide dead or unconscious, nobody activated the suppression field so Becket was able to telekinetically open the Amplifier and extend the bridge.