Oblivious Random Access Machines (ORAMs) allow cloud users to access remote data without leaking access patterns. Current ORAM solutions achieve this goal at expense of either increasing bandwidth consumption by a factor of$O(\log N)$, where$N$is the number of data blocks, or relying on homomorphic encryption for bandwidth amplification reduction to$O(1)$. Furthermore, most ORAMs are only effective for a single user, while the solutions for multi-user scenarios often induce security or performance problems. This article introducesTianji— an asynchronous multi-user Shamir-based ORAM system — which supports asynchronous network access scenarios for multiple users with improved security and performance.Tianjiis implemented on top ofS$^{3}$3ORAM$^+$+—an extension of the state-of-the-art Shamir-based S$^{3}$ORAM with a new non-eviction data write-back scheme to achieve$O(1)$consumption in both bandwidth amplification and storage capacity. Our experimental results show that the proposedTianjiwithS$^{3}$3ORAM$^+$+can significantly outperform the state-of-the-art multi-userTaoStorein terms of access latency and client scalability. Additionally, its average response time is relatively stable when client loads increase.