Sure, at the price of violating the 5th Amendment (eminent domain clause). Also probably at the price of the future productivity of those 30% of companies (government owners usually turn out to not be very efficient managers).
Who said anything about managing?
Govt should merely own shares (30%, or more, of each company, not 30% of companies), and let existing capitalist/free-market incentives continue to do what they're good at, driving innovation and efficiency.
While replacing, at least partly, what they're not good at, which is distributing the profits fairly to all contributors, and supporting the wider society that enables them to operate at all.