There have been prior threads on this, but I cannot come up with search terms that work. In essence: An overdraft is a loan. Business entities; e.g. corporations, partnerships, LLCs, etc. borrow money by adopting resolutions authorizing named individuals to borrow money. A person authorized to sign on an account is not necessarily empowered to borrow money.
This would require a great deal of thought and some significant ingenuity. Even then, it might not be a great idea...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.