Well, in case of a bank it can. And it happens on a daily basis. In fact thats how most private bank money enters the system in the first place either when a bank makes a loan or when it buys any other asset like e.g. a corporate bond (you can conceptualize a loan as an asset purchase as well, the bank buys a promise to pay from the borrower which is recorded as an asset of the bank). Both are a balance sheet extension from a double-entry bookkeeping point of view.
The 4 operations double-entry bookkeeping allows are:
1. balance sheet extension (e.g. making a loan) 2. balance sheet reduction (e.g. loan repayment) 3. asset swap (e.g. a bank buying a government bond with central bank reserves) 4. liability swap (e.g. transferring money from one account to another)
So it may be more accurate to just say that every event that affects the balance sheet must be one of those 4 operations.
Also see "Money creation in the modern economy" - Bank of England Quarterly Bulletin 2014 Q1