A multi-stage distillation system includes multiple stages, and each stage Si includes an evaporator Ei and a condenser Ci. Each condenser includes a steam chamber in pressure-connection with a steam chamber of each evaporator of the same stage. Each evaporator has a steam chamber outlet connected to a spray inlet of the next evaporator Ei+1, and the outlet of the last evaporator En connects to the spray inlet of the first evaporator E1 with a respective fluid line to form an evaporator circuit. Each outlet of each condenser Ci connects to the one spray inlet of the previous condenser Ci−1, and the outlet of the first condenser C1 connects to the spray inlet of the last condenser Cn with a fluid line to form a condenser circuit. A steam line connects between condensers Ci+1 and Ci or between the evaporators En and E1.