A stacked pump arrangement for mixed-media flow includes a first, self-priming, centrifugal pump with a volute having an inlet and an outlet and a second straight centrifugal pump mounted to an upper portion of the first centrifugal pump, the second straight centrifugal pump also having a volute with an inlet and an outlet. A transition chamber is connected, at one end, to the first centrifugal pump volute outlet and is connected, at another end, to the second straight centrifugal pump volute inlet.