Software in modern vehicles consists of multi-criticality functions, where a function can be safety-critical with stringent real-time requirements, less critical from the vehicle operation perspective, but still with real-time requirements, or not critical at all. Next-generation autonomous vehicles will require higher computational power to run multi-criticality functions and such a power can only be provided by parallel computing platforms such as multi-core architectures. However, current model-based software development solutions and related modelling languages have not been designed to effectively deal with challenges specific of multi-core, such as core-interdependency and controlled allocation of software to hardware. In this paper, we report on the evolution of the Rubus Component Model for the modelling, analysis, and development of vehicular software systems with multi-criticality for deployment on multi-core platforms. Our goal is to provide a lightweight and technology-preserving transition from model-based software development for single-core to multi-core. This is achieved by evolving the Rubus Component Model to capture explicit concepts for multi-core and parallel hardware and for expressing variable criticality of software functions. The paper illustrates these contributions through an industrial application in the vehicular domain.