Very, very good question. I have been thinking about that, too. It's a head scratcher and it sharpens the discussion. You could correctly frame the republican discussion as a really garbled version of this. The "people" framed as the agency "incorporating" the state to do their biding, as opposed to the sovereign (king.) The state and the king then becoming separate entities. But is it possible to have a sovereign corporation. A sovereign legal entity? it would seem a contradiction in terms. How can the entity recognize *itself* as a legal person? There has to be something outside it to do that.
I don't think the sovereign can be a corporation, for this reason. The sovereign is a "legal entity," insofar as each new sovereign doesn't just spring from the ground and rule based completely on his own, spontaneously and unanimously recognized capacities. Like any role, the sovereign is defined by that role: a "shoemaker" is also a "legal entity," even if not in the same terms as a corporation. What makes the sovereign a legal entity is that he defines, recognizes and constrains all the other entities in the tradition of sovereignty over those entities. That's the "outside": being both the source and effect of the legal traditions.