We propose inheritance and refinement relations for a CSP-based component model (BRIC), which supports a constructive design based on composition rules that preserve classical concurrency properties such as deadlock freedom. The proposed relations allow extension of functionality, whilst preserving behavioural properties. A notion of extensibility is defined on top of a behavioural relation called convergence, which distinguishes inputs from outputs and the context where they are communicated, allowing extensions to reuse existing events with different purposes. We mechanise the strategy for extensibility verification using the FDR4 tool, and illustrate our results with an autonomous healthcare robot case study.