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All-optical re-switching has been investigated in the half-metallic Heusler ferrimagnet Mn2Ru0.9Ga, where Mn atoms occupy two inequivalent sites in the XA-type structure. The effect of a second 200 fs 800 nm pump pulse that follows a first pulse, when both are above the threshold for switching, is studied as a function of t12, the time between them. The aims are to identify the physical mechanisms involved and to determine the minimum time needed for re-switching. The time trajectory of the switching process on a plot of sublattice angular momentum, S4a vs S4c, is in three stages; When t < 0.1 ps, the sublattice moments are rapidly disordered, but not destroyed, while conserving net angular momentum via optical spin-wave excitations. This leads to transient parallel alignment of the residual Mn spins in the first quadrant. The net angular momentum associated with the majority sublattice then flips in about 2 ps, and a fully-reversed ferrimagnetic state is then established via the spin-lattice interaction, which allows re-switching provided t12 > 10 ps.