Split the US dollar into 2 currencies, an exchange currency and a deposit currency. The deposit currency would not be distributed, would be more or less a fixed amount, and have very stringent rules preventing any form of "policy" from being applied to it. The exchange currency would be managed much as the US dollar is now, allowing the central bank to managed it as necessary for the economic situation from moment to moment.
Savings deposits would to converted to deposit currency at whatever the going rate between the two is and held outside of inflation cause by management of the exchange currency. The Fed window would be ended and replaced by open auction system where the Fed would auction lend-able money to the highest interest rate bidder that is a qualifying lending institution. Interest paid back to the Fed would be returned to holders of the depository currency, The returned interest could alternatively be taxed, or used to fight inflation in the exchange currency.
Effectively this ends the Fractional Reserve system and replaces it with a Fractional currency system. Banks would no longer be able to lend more money then they posses. But they still would be able to act as a intermediary servicing agent for the central bank when addition market liquidity is needed.