This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN. This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by applying efficient switching algorithms. This approach has many practical applications. First and foremost, it becomes an integral tool for the recent standardization initiatives of homomorphic schemes and common APIs. Then, it can be used in many real-life scenarios where operations of different nature and not achievable within a single FHE scheme have to be performed and where it is important to efficiently switch from one scheme to another. Finally, as a byproduct of our analysis we introduce the notion of a FHE module structure, that generalizes the notion of the external product, but can certainly be of independent interest in future research in FHE.