That mixture is like a woman trying to be both pregnant and not pregnant. By definition, not possible.
You are either free under capitalism or slaves under socialism (or one of the other Totalitarian derivatives)
Indirect control of the means of production is Fascism, TF. We have significant elements of fascist structure in our government and have done since FDR. We also have capitalistic and socialistic elements.
That would make our government a Progressive mixed government. For myself, I prefer the original mix of democratic, oligarchic and monarchic.