That's basically the thinking behind some of the flavor of market socialism. Allow private companies, and allow or even encourage market competition in many are

That's basically the thinking behind some of the flavor of market socialism. Allow private companies, and allow or even encourage market competition in many areas, but have some mechanism by which large, established companies move to be increasingly publically controlled over time such that the purely profit seeking behavior can be overridden. Of course, the devil is very much in the details.