Is this a feasible business structure?

Say I own a business that has four reasonably distinct divisions. Can I split up the company into four separate, independent businesses, each run by the current division manager who would then be his own boss with equity in his respective division. I would then become the main "investor"/majority equity holder in each individual company.

This way I would still own the business, but I think the individual managers would have much more incentive to perform than if you just gave them a small sliver of equity in the entire consolidated business?

I'm sure this has been done before, and maybe there are some large companies structured like this. What do you guys things? What are the pros/cons of this?