Aircraft cabin air conditioning system, comprising: - a first motorized turbomachine, referred to as a water extraction turbomachine, comprising a compressor, a water extraction turbine comprising an outlet and an inlet, and a motor driving the compressor and the water extraction turbine in rotation, - a second motorized turbomachine, referred to as a cooling turbomachine, comprising a compressor, a cooling turbine comprising an inlet and an outlet, and a motor driving the compressor and the cooling turbine in rotation, - a water extraction loop connected to the inlet of the water extraction turbine and comprising a condenser (30a; 30b) and a water separator, - an outlet from the air conditioning system, configured such that it can be connected to the cabin of the aircraft the compressor of the water extraction turbomachine and the compressor of the cooling turbomachine being configured to receive air outside the aircraft and being mounted in parallel so as to be able to feed a common outlet, the water extraction turbine and the cooling turbine being mounted in series such that the outlet of the water extraction turbine is fluidly connected to the inlet of the cooling turbine, and the outlet of the cooling turbine being connected to the outlet of the air conditioning system, the air conditioning system being characterized in that it comprises a network of pipes and associated valves, fluidly connected to the common outlet of the compressors and making it possible to supply, from the common outlet of the compressors: - either the inlet of the water extraction turbine, - or the inlet of the cooling turbine, bypassing the water extraction turbine and the water extraction loop, - or, directly, the outlet of the air conditioning system, bypassing the cooling turbine, the water extraction turbine and the water extraction loop. - a first motorized turbomachine, referred to as a water extraction turbomachine, comprising a compressor, a water extraction turbine comprising an outlet and an inlet, and a motor driving the compressor and the water extraction turbine in rotation, - a second motorized turbomachine, referred to as a cooling turbomachine, comprising a compressor, a cooling turbine comprising an inlet and an outlet, and a motor driving the compressor and the cooling turbine in rotation, - a water extraction loop connected to the inlet of the water extraction turbine and comprising a condenser (30a; 30b) and a water separator, - an outlet from the air conditioning system, configured such that it can be connected to the cabin of the aircraft the compressor of the water extraction turbomachine and the compressor of the cooling turbomachine being configured to receive air outside the aircraft and being mounted in parallel so as to be able to feed a common outlet, the water extraction turbine and the cooling turbine being mounted in series such that the outlet of the water extraction turbine is fluidly connected to the inlet of the cooling turbine, and the outlet of the cooling turbine being connected to the outlet of the air conditioning system, the air conditioning system being characterized in that it comprises a network of pipes and associated valves, fluidly connected to the common outlet of the compressors and making it possible to supply, from the common outlet of the compressors: - either the inlet of the water extraction turbine, - or the inlet of the cooling turbine, bypassing the water extraction turbine and the water extraction loop, - or, directly, the outlet of the air conditioning system, bypassing the cooling turbine, the water extraction turbine and the water extraction loop. - either the inlet of the water extraction turbine, - or the inlet of the cooling turbine, bypassing the water extraction turbine and the water extraction loop, - or, directly, the outlet of the air conditioning system, bypassing the cooling turbine, the water extraction turbine and the water extraction loop.