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Additionally there is prison labor which is legal in the U.S. to force someone to do.

Prison labor allows companies to purchase labor at a rate the non-incarcerated worker can't afford to sell their labor at.

>Should a company be allowed to own slaves?

No, because slavery is illegal.

>Should a company be allowed to do business with a company that owns slaves?

They do, all the time. Manufacturing, mining (particularly of the rare earth metals that go into electronics) and agriculture all depend on slave labor.

Should the second one be illegal as well?

What is the functional difference between the two besides more paperwork and another middle man taking a cut?

It certainly should be illegal, but a lot of the comforts of first-world civilization would vanish and the velocity of modern capitalism would grind to a halt, so politically speaking apart from token gestures that don't threaten the status quo that isn't likely to happen.

I think generally owning slaves goes against the idea of freedom (let's discard the concept one has the freedom to sell themselves for once). Thus company does not have the right to own slaves.