Cloud-native database systems with multi-primary shared-storage architecture have emerged due to their superior performance over primary-secondary architecture on write-intensive workload scenarios. However, these systems face performance degradation as the proportion of shared data increases, adversely affecting their Cost-Performance Ratio (CPR). In this paper, we identify frequent page ownership transfers between primaries as a key factor contributing to these performance bottlenecks. To address this challenge, we propose Chimera, a multi-primary database system that employs a two-phase transaction scheduling mechanism, combined with a delay-fetch ownership transfer strategy to effectively reduce the overhead of ownership transfers. Extensive experiments on SmallBank and TPC-C benchmarks demonstrate that Chimera outperforms existing schedule methods for multi-primary systems, achieving performance gains of 1.86× ~19.03× on throughput.