The invention relates mainly to a pumping system (1) which comprises an alternating distribution device comprising at least one shut-off device (7) comprising four mobile shut-off members (70-73) for shutting off first and second inlets (E1, E2; E1a, E2a) and first and second outlets (S1, S2; S1a, S2a) of the pumping system (1) and at least one trigger (8, 9) configured to actuate said shut-off members (70-73) between two positions, respectively a shutting-off position and an open position, which alternating distribution device can be actuated between a first arrangement associated with a first fluid distribution cycle and a second arrangement associated with a second fluid distribution cycle.