Yes, banks can "cross-collateralize" more than one loan with the same borrower(s), if the loan documents the borrower(s) signed agree that the bank can do this. You'll need to review the loan documents to see what you've agreed to.
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Local credit unions rountinely have these cross collateralization clauses. Other banks often do not. you need to review the paperwork to determine whether it states that the collateral pledge as security for one loan also secures any other obligation to that lender.