By allowing a large number of users to behave as readers or writers, Multi-User Searchable Encryption (MUSE) raises new security and performance challenges beyond the typical requirements of Symmetric Searchable Encryption (SSE). In this paper we identify two core mandatory requirements of MUSE protocols being privacy in face of users colluding with the CSP and low complexity for the users, pointing that no existing MUSE protocol satisfies these two requirements at the same time. We then come up with the first MUSE protocol that satisfies both of them. The design of the protocol also includes new constructions for a secure variant of Bloom Filters (BFs) and multi-query Oblivious Transfer (OT).