In this paper we propose a synchronization protocol for resource sharing among independently-developed real-time systems on multi-coreplatforms. The systems may use different scheduling policies and they may have their own local priority settings. Each system is allocated on a dedicated processor (core). In the proposed synchronization protocol, each system is abstracted by an interface which abstracts the information needed for supporting global resources. The protocol facilitates the composability of various real-time systems with different scheduling and priority settings on a multi-core platform. We have performed experimental evaluations and compared the performance of our proposed protocol (MSOS) against the two existing synchronization protocols MPCP and FMLP. The results show that the new synchronization protocol enables composability without any significant loss of performance. In fact, in most cases the new protocol performs better than at least one of the other two synchronization protocols. Hence, we believe that the proposed protocol is a viable solution for synchronization among independently-developedreal-time systems executing on a multi-core platform.