Rupert, Lachlan and their allies are trying to do that in the Nevada courts currently. But the first lawsuit ended with a judgement that upheld the rights of the three liberal children. He is now preparing to appeal that. However, if I remember correctly, the entire arrangement only applies if Rupert Murdoch dies before 2030 (or so), so if he lives longer than that, he may be able to arrange his legacy in whatever way he desires.

Control over Rupert Murdoch’s media empire will probably pass to four of his children, with equal voting rights for all of them. Only one of them (Lachlan) is as right-wing as he is. The other three are comparatively liberal, e.g. they consider man-made climate change a threat. Long-form story: https://www.theatlantic.com/magazine/archive/2025/04/rupert-murdoch-family-succession-james-murdoch/681675/