A CO2 cooling system includes a compression stage in which CO2 refrigerant is compressed; a cooling stage in which the CO2 refrigerant releases heat; a CO2 liquid receiver in which the CO2 refrigerant is accumulated in liquid and gaseous states; an evaporation stage in which the CO2 refrigerant, having released heat in the cooling stage, absorbs heat. The evaporation stage has first and second evaporation sectors; a first metering device for feeding CO2 refrigerant into the first evaporation sector at a first pressure; and a second metering device for feeding CO2 refrigerant into the second evaporation sector at a second pressure. The first metering device and the second metering device are operated independently from one another. A plurality of CO2 transfer lines connects the compression stage, the cooling stage, the CO2 liquid receiver and the evaporation stage. The CO2 refrigerant is circulable in a closed-loop circuit.