A mop or like cleaning implement with a fluid reservoir and dispensing handle and with an integral refill/add-on reservoir receiver which embraces the handle. A refill/add on reservoir fluid container is inserted into the receiver to supplement and/or replenish the volume of liquid contained in the fluid reservoir handle. The refill fluid container can be removed and replaced when empty. The reservoir and dispensing handle can be filled and refilled independently of the refill fluid container, or can be refilled using the refill container. Either way, a refill container can be inserted into the refill receiver to supplement the volume of fluid in the reservoir handle.