Industry and other sectors are currently looking for solutions to decarbonize their processes, including heating, which is mainly based on fossil fuel boilers. Heat pumps can provide heating with higher performance based on their high coefficient of performance (COP). This work considers a multilevel heat pump (MTHP) for multi-source heating, based on a three-stage cascade in which excess heat in the condenser is used for external flows, that can be connected in series or parallel. Several available low GWP refrigerants have been considered, and a multi-parameter selection analysis has been carried out. For low, medium, and high-temperature stages, R1243zf, R-1224yd(Z), and R-1233zd(E) are the best refrigerants, respectively, selected. This system is able to operate between 0 and 160 degrees C, with three heating levels at 60, 110, 160 degrees C (31.75, 21.59, and 29.92 kW, respectively) at a COP of 2.181. The total cooling capacity of the system is 45.08 kW and the total heating capacity is 83.26 kW. The MTHP concept can provide a significant carbon footprint reduction compared to natural gas boilers used in European countries.