What if Stalin for some reason got fed up with Beria and decided to kill him? How could Beria push Stalin to the point of getting himself purged? Stalin has supposedly collecting evidence on Beria's sexual assaults, which could suggest he was planning to go after Beria, and that means it wouldn't take much to just have Stalin kill him in my opinion. I could see Beria raping Stalin's daughter(Stalin was once informed of his daughter being at Beria's home alone, said he didn't trust Beria, and called her and told her to leave.), and getting himself executed or sent to his own gulags for it.