Over the last few years, the improved performances of FHE has paved the way for new multi-user approaches which go beyond performing encrypted-domain calculation for a single user. In this context, this paper proposes several simplified multi-user setups resulting in new FHE-based building blocks and protocols. By $simplified$ $multi$-$user$ setting we mean that, in order to process a user request, the FHE server is able to select only data encrypted under the proper key in an oblivious way. In doing so, information like the distribution of data per user remains private without losing the consistency of the obtained homomorphic results. We conclude the paper with experiments illustrating that these simplified setups, although not universally applicable, can lead to practical performances for moderate-size databases.