No private entity has the right to conduct war.

Yes, but under international law that nice thick line starts to show some wear and tear.

Mercenaries are not accorded the rights of lawful combatants in the Geneva convention, however so long as private military personnel are:

1. Nominally acting under the authority of a state authority.

2. Nationals of a state that is party to the conflict.

Thus, Blackwater in Iraq was legally an agent of the US government, so that where it employed Ukranians as employees they were lawful combatants (because Ukraine was a party to the conflict), but when they brought in former South African special forces they employed unlawful combatants, because South Africa wasn't party to the conflict.

Murky, eh?

And what happens when the size of the these PMCs armed contingents is larger than the local army?

And I'll give my consent to any government that does not deny a man a living wage-Billy Bragg

The answer isn't a world without power, it's one in which power has a social purpose.

Which means combating neoliberal ideology, recapturing governments from the moneyed interests, and using them to create a better world.

If the US and European governments are on the same page about the world that they want than then that is the world that we will have.

It seems to me that the rage for civil society solutions has at least something to do with economic elites control over the machinery of state when the franchise was extended.  Because they've lost at the game of political democracy, they think that they can slip the leash by undermining national systems that regulate economies........

And I'll give my consent to any government that does not deny a man a living wage-Billy Bragg