The growing complexity of embedded systems software entails new development techniques. Component-Based Software Engineering is undoubtedly suitable for the development of complex systems thanks to its inherent component reuse. Another approach to reduce software complexity is by partitioning the system behavior into different operational modes. Each mode is associated with a unique behavior and the system can change behavior by switching between modes. When such a multi-mode system is developed by reusable software components, a crucial issue is how to achieve a seamless composition of multi-mode components and also how to handle mode switch properly. As an integrated solution to the challenges of multi-mode component-based software system development we have proposed the Mode Switch Logic (MSL). The current version of MSL assumes independent handling of a single mode switch scenario, i.e. that no other mode switch is triggered until an ongoing mode switch is completed. For a wide class of systems, this is an unrealistic assumption. In this report we lift this assumption by proposing an extension of MSL to handle multiple mode switch scenarios concurrently triggered by different components.