To support simultaneous multicasting and unicasting service, a 2-level superposition coded modulation (SCM) system with variable code rate allocation is studied. To obtain the most power-efficient scheme for this system, brute-force method can be used to find the best power allocation for each code rate allocation. However, it is very complicated and time-consuming. In this work, the properties of the 2-level SCM capacity is first studied using numerical evaluation and a heuristic method is proposed to efficiently find the optimal rate assignment and power allocation. The simulation results verify the performance of the proposed power allocation method and experimental results show that equal rate allocation scheme provides a power-efficient transmission.