A pump device for an internal combustion engine, having a high-pressure fuel pump for supplying fuel to a first injection device, having at least one low-pressure inlet, via which the fuel is fed to the high-pressure fuel pump from a low-pressure fuel pump, having at least one low-pressure outlet for conducting the fuel conveyed by the low-pressure fuel pump and fed via the low-pressure inlet to the high-pressure fuel pump out of the high-pressure fuel pump, and having at least one low-pressure port, for conducting fuel conveyed by the low-pressure fuel pump to a second injection device. At least one mixing region mixes the fuel flowing through the low-pressure outlet with fuel fed to the mixing region from the low-pressure fuel pump upstream of the high-pressure fuel pump. The low-pressure port is fluidically connected to the mixing region, and the low-pressure inlet is supplied with fuel from the mixing region.