Problem is historically control is expensive and almost impossible. the best thing a corporation can do is make peopel feel as free as possible, make them feel as though they have the freedom while your simply presenting them with choices you want.
with that said I envision a democratic system, controlled by corporations. much like today except people dont see it as dirty and vile to accept their money. there a a bunch of different corporations who endorse senators and let them more or less have their run of things on two conditions. The Senators keep the markets free and growing, finding new resources for the hungry industries of progress, and 2 they avoid all the anti business regulations that choke business and slow their growth. and should a Senator rise up and try to expose these situations, that senator could meet a number of disgraceful ends, or even death. That is much more corporate like, they dont want to flaunt public control, they want money, and they are much better letting someone else pretend to be in power while they make deals in the background.
besides direct control is expensive, and when people get angry and unruly it would be the corporation who has to step in, spend its own money and risk its own public reputation. a shield is always better.