The only solution I can see is through legislation, strictly forbidding and creating institutions to prevent corporate interferance in government.
Some measures:
1) Outlawing lobbying more broadly, improving campaign financing, etc.
2) Reforming the government to promote greater adaptability and efficiency, mimicking how companies improve themselves through competition.
There are quite a few examples of countries with good control over corporations (Japan I think is quite strict at least in terms of election financing and advertising), and good alignment of government and human values. But many others, notably by the US, turn more and more the opposite way towards corporate/economic absolutism.
It's been said before, but people put a little too much fear into AI takeover when gigantic, scalable, self-improving systems with trivial values (economic output) are already almost taking over the world.
Fear The Corporation.