This article presents a multilevel design for spin-orbit torque (SOT)-assisted spin-transfer torque (STT)-based 4-bit magnetic random access memory (MRAM). Multilevel cell (MLC) design is an effective solution to increase the storage capacity of MRAM. The conventional SOT-MRAMs enable an energy-efficient, fast, and reliable write operation. However, unlike STT-MRAM, these cells take more area and require two access transistors per cell. This poses significant challenges in the use of SOT-MRAMs for high-density memory applications. To address these issues, we propose an MLC that can store 4 bits and requires only three access transistors. The effective area per bit of the proposed cell is nearly 58% lower than that of the conventional 1-bit SOT-MRAM cell. The combined effect of SOT and STT has been incorporated to design SOT-STT-based MLC that enables more energy-efficient and faster write operation than the regular MLCs. The results show that SOT-STT-based 4-bit MLC is 52.9% and 40% more efficient in terms of latency and energy consumption, respectively, when compared to 3-bit SOT-/STT-based MLC.