Single-master multi-slave is the mainstream architecture of cloud-native databases. In the cluster, slave nodes can share the read-only requests of the master node, while write requests are handled by the master node. Based on this, to further meet the demands of large-scale transaction expansion, some cloud databases attempt to implement multi-write transaction expansion. One possible approach to multi-write expansion is to introduce shared cache among computing nodes to support cross-node data access. For shared-cache database systems, the overhead of cross-node remote access is significantly higher than that of local access. Therefore, the design of cache protocol is a crucial factor that affects system performance and scalability. This study proposes two innovative improvements to the coherence protocol and implements PG-RAC, a shared-cache database, which supports multi-write transactions based on PostgreSQL. On one hand, PG-RAC proposes a new distributed chained routing strategy, which disperses routing information among computing nodes. Compared to the routing strategy that utilizes single-node directory management, it reduces the average transaction latency by approximately 20%. On the other hand, this study also enhances the duplicate page invalidation mechanism by separating invalidation operations from the transaction path, reducing the latency of the critical path in the transaction. Based on this, PG-RAC takes advantage of the characteristics of multi-version concurrency control (MVCC) and further proposes to delay the invalidation point of duplicate pages, which effectively improves cache utilization. TPC-C experimental results show that for a cluster with 4 compute nodes, the throughput is nearly 2 times that of PostgreSQL and 1.5 times that of the distributed database Citus.