A multistage thermal desalination system, together with its associated method of use, allows de-scaling of subsystems exposed to saturated saltwater by alternating the saturation stage of the process between two neighboring physical desalination stages. The desalination system is provided with at least one transfer conduit, at least one pump, and valving to permit saltwaters being desalinated by higher and lower stage desalination subsystems to be swapped. By replacing the saturated saltwater in a higher salt concentration desalination subsystem with lower salt concentration saltwater, the scaling in higher salt concentration desalination subsystem is reduced while the saturation load is placed on another of the desalination subsystems.