A multi-stage diaphragm suction pump, includes at least two pump chambers, each having a inlet having at least one inlet valve, and a outlet having at least one outlet valve, and a suction line, which connects the fluid inlets of the pump chambers. Successive pump chambers are connected to one another by at least one connection line such that, when a differential pressure in the suction line is reached/exceeded, the diaphragm pump changes from parallel to an operating mode that is at least also serial. At least one check valve, which opens to a downstream pump stage, is interposed in each of the inflow and outflow regions of the at least one connection line. A suction-side opening or a pressure-side opening of the connection line is arranged in a region of the pump chamber on which a diaphragm associated with the pump chamber rolls first during a pump cycle.