Conventional single-junction solar cells have a theoretical efficiency limit around 33%, and multi-junction solar cells (MJSCs) are currently the only technology to overcome this limit. The demonstration of hot-carrier solar cells (HCSCs), another high-efficiency approach that relies on harvesting the kinetic energy of the photo-generated carriers, has so far been hindered due to the difficulty of mitigating carriers' thermalization. In this letter, we highlight the synergies of these two concepts by introducing the hot-carrier multi-junction solar cell (HCMJSC), a MJSC with a thin hot-carrier top junction. Using a detailed balance model, we compare the efficiency of different devices as a function of three parameters: the bandgap of the top and bottom junctions, the top cell thickness, and an effective thermalization coefficient, which encapsulates information on both thermalization and light trapping. Besides allowing for a much broader range of material combinations than MJSCs, we show that HCMJSCs can reach efficiencies higher than MJSCs with a larger thermalization coefficient than HCSCs. As such, HCMJSCs could provide a preferred route toward the development of hot-carrier-based high efficiency devices.