The present invention belongs to the technological field of cooling systems. A multiple-evaporation cooling system with two or more evaporation lines is disclosed. In a first intermediate heat exchanger (62), the first evaporation line (Levap1), preferably the portion defined between the evaporator (51) and the suction inlet (11) of the compressor (1), is in heat exchanging contact with at least one segment of the expansion device (42) of the second evaporation line. In a second intermediate heat exchanger (61), the second evaporation line (Levap2), preferably the portion defined between the evaporator (52) and the suction inlet (12) of the compressor (1), is in heat exchanging contact with at least one segment of the expansion device (41) of the first evaporation line. The temperature of the intermediate heat exchanger of first evaporation line (62) influences the temperature of the refrigerant flowing in the second line of evaporative expansion device (42) and the temperature of the intermediate heat exchanger of the second evaporative line (61) influences the temperature of the refrigerant flowing in the first line of evaporative expansion device (41). The invention in question is distinguished for varying the restriction of the respective expansion devices (41,42) and then unduly inhibit mass transfer of refrigerant between at least two distinct evaporators (51,52).