It would be interesting to see the Lucavi try to take over Sakura. Considering the greater grail probably watches over her as the ideal vessel at the time...
So she'd kill Shinji after he turns Lucavi. Sakura takes the holy stone by instinct, believing she could justify self-defense by showing it to people that it turned Shinji into a monster she had to kill. Meeting with Zouken who is less than disappointed with her killing Shinji nudges her psychologically. She locks herself in her room rationalizing herself. Thinking maybe if she acted like it never happened then it would be fine. But the voice of the lucavi speak through the stone. It pierces through the veil of deceit she put over her heart. It exposes all her secrets and gleefully watches her break apart enough to wish it would take her place. The grail does not allow it and fights back, telling Sakura that her purpose is set. This just puts her further on edge. When Rider returns to her and Zouken realizes Sakura is practically withdrawing from the war, he takes measures to force her into battle, starting by killibg the weakest master; Emiya. That just breaks Sakura and the holy stone begins to react and the grail follows suit. She becomes possessed by the Lucavi but not to the point of destroying her as the grail has taken root in her as all the world's evils. The powers clash violently but they compliment each other giving Sakura more than enough power to annihilate Zouken. The grail wishes to be born but so do the lucavi wish for Ultima's return. The two wishes gnaw away at Sakura who is already frazzled and she pushes their plans away. All she wants is a place to belong so she begins to look for people to accept her, all of her.