The present study deals with a compression-absorption machine. The proposed hybrid cooling system uses water-ammonia as a working fluid and operates at three pressure levels. The absorber is at an intermediate pressure (Pint) taken between the evaporator pressure (PEV) and the condenser pressure (PCD), unlike the single stage machine which works between two pressure levels. The proposed new system is studied and compared to the conventional machine. In order to evaluate the performance of the invoked machine, a procedure based on the MAPLE software is set up to compute accurately the thermodynamic properties of the working fluid. The analyses of the numerical results highlight that the performance of the novel proposed configuration is better than that relative to the conventional system. The study reveals the great impact of the intermediate pressure on the performance improvement and on reducing the generator temperature allowing the system to work at low enthalpy. In fact, for an evaporator temperature and a condenser temperature fixed respectively at -10°C and 40°C, the proposed hybrid refrigeration cycle operates at a generator temperature TGE = 75°C and the installation’s COP is about 0.56. While for the same conditions, the single stage machine COP cannot exceed 0.51 with a generator temperature of about 135°C. Consequently, our enhanced novel configuration presents the opportunity to operate at low enthalpy sources.