Component-Based Development (CBD) reduces development time and effort by allowing systems to be built from pre-developed reusable components. A classical approach to reduce embedded systems design and run-time complexity is to partition the behavior into a set of major system modes. In supporting system modes in CBD, a key issue is seamless composition of multi-mode components into systems. In addressing this issue, we previously developed a Mode Switch Logic (MSL) for component-based multi-mode systems. Our MSL implements seamless coordination and synchronization of mode switch in systems composed of independently developed components. However, our original MSL is based on the, in a setting of reusable components, unrealistic assumption, that all the components of a system support the same modes. This considerably limits the feasibility of our MSL. In this paper we lift this assumption and propose a mode mapping mechanism that enables assembly of components supporting different sets of modes. We demonstrate our mode mapping mechanism by a simple example application.