In recent years, the concept of the Reality-Virtuality Continuum (RVC) has taken a central role in research on immersive technologies, delineating the spectrum between physical and virtual reality. However, while Augmented Reality (AR) and Virtual Reality (VR) have reached a technological maturity, existing solutions tend to be constrained to specific devices or use cases, limiting the possibilities for collaboration. In this context, the Cross-Reality (CR) paradigm aims to overcome such barriers, offering seamless integration between desktop devices, mobile AR, and immersive VR headsets. This paper introduces CrossWarp, a framework designed to enable real-time collaboration experiences between users with different devices within a common virtual space. The framework adds support for a smooth transition of digital objects between different realities, preserving state and context, facilitates interoperability between heterogeneous platforms, enabling hybrid interactions between desktop and mobile AR, and provides flexibility and extensibility, adapting to different application domains.