Will the quantity of money available increase when banks keep their reserves with the reserve bank?

In the US, if a customer deposits currency at a retail bank, the bank will be permitted to issue up to about 10 times the value of the currency in the form of checking and savings funds. One might wonder if the same money multiplier rule applies to the Fed, which is the banker's bank.

In fact, it does not: Reserves in the form of current Federal Reserve Notes (wads of greenbacks) are liabilities of the Fed. Therefore the Fed's financial position does not change when a member bank deposits cash into it. The cash is already debt of the Fed. The Fed merely converts the notes to more reserve credit balances.

However, the Fed is permitted to increase the money supply by purchasing notes from the member banks which mature in the future. In such a transaction, the member bank is posting non-current notes as collateral and the Fed is advancing credit balances payable in current Federal Reserve Notes. If one wants to consider such a transaction to be a deposit, then it is fair to say that this does increase the amount of money in circulation.