This paper proposes MUREX, a mutable replica control scheme, to keep one-copy equivalence for synchronous replication in structured P2P storage systems. For synchronous replication in P2P networks, it is proper to adopt crash-recovery as the fault model; that is, nodes are fail-stop and can recover and rejoin the system after synchronizing their state with other active nodes. In addition to the state synchronization problem, we identify other two problems to solve for synchronous replication in P2P storage systems. They are the replica acquisition and the replica migration problems. On the basis of multi-column read/write quorums, MUREX conquers the problems by the replica pointer, the on-demand replica regeneration, and the leased lock techniques.