If you want to form a "private corporation" you march down to your state office or branch of the secretary of state for that state and fill out and file "articles of incorporation". It's not just for "public corporations" that wish to issue stock. Both private and public corporations are legal fictions (persons) created by charter/contract with the government.
"If the lending private bank is not a corporation, who will sign agreement between 1) lender=joint agreement of lenders and 2) borrower= joint corporate agreement of borrowers?"
The contracts between individuals that make up any joint partnership (including banks) would detail which partners and how many would need to sign and how new partners would be integrated into or removed from the joint partnership contract scheme.
~wobbles but doesn't fall down~
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