The combination of multi-stage heat pump cycles with small-scale oil-free turbocompressor technology running on gas bearings could be a promising way to increase performance in domestic and commercial heat pumps. This paper presents a novel two-stage heat pump system with two heat sources at two different temperature levels using two separate turbocompressors rotating on gas bearings optimized for R134a. The system allows integration of unused heat sources, e.g. solar thermal or waste heat, into heat production with a minimal loss of exergy. The cycle comprises an evaporator for the first heat source, a condenser as heat sink, an open economizer with integrated heat exchanger for the second heat source, and a tube-in-tube suction line heat exchanger (SHX) in the high-pressure for superheating and subcooling. The aim of this study is to evaluate theoretically the performance of this heat pump cycle using a system model programmed in the software EES (Engineering Equations Solver). The simulation assumes steady-state, negligible pressure drops and heat losses, and adiabatic expansion processes. The superheating in the evaporator and the SHX is 5°C, and there is no subcooling in the condenser. The heat exchangers are modeled using effectiveness-NTU models. At the design point, the heating capacity of the condenser is set to 6.5 kW and provides hot water of 55°C. The first heat source is brine of 5°C. The second heat source is water of 30°C and has been designed to provide up to 30% of the total condenser heat capacity. The two turbocompressors are designed specifically to meet the heat pump design point. Presently, one-dimensional (1D) compressor maps are used in the heat pump model. Simulation results show that coefficient of performance (COP) improvements of 20% to 30% are achievable, depending on the source temperature levels of the heat pump cycle and the amount of second heat source added to the system. The COP increases with higher source temperatures, higher second heat source capacity, and lower sink temperature. The pressure ratios are defined by the imposed temperature levels. The mass flow rate of the refrigerant in the first stage is mainly determined by the second heat source capacity, and in the second stage by the heat capacity of the condenser. In future work, this novel heat pump concept will be tested experimentally.