How to maximize the advantages of in-network caching under limited cache space has always been a key issue in information-centric networking (ICN). Replica placement strategies aim to fully utilize cache resources by optimizing the location and quantity distribution of replicas in the network, thereby improving the performance of the cache system. However, existing research primarily focuses on optimizing the placement of replicas along the content delivery path, which cannot avoid the inherent drawback of not being able to leverage off-path cache resources. The proposals for off-path caching cannot effectively solve this problem as they introduce excessive complexity and cooperation costs. In this paper, we address the trade-off between cache resource utilization and cooperation costs by introducing a mechanism complementary to replica placement. Instead of redesigning a new caching strategy from scratch, we propose a proactive cooperative caching mechanism (called RMBCC) that involves an independent replica migration process, through which we proactively relocate replicas evicted from the local cache to neighboring nodes with sufficient cache resources. The cooperation costs are effectively controlled through migration replica filtering, migration distance limitation, as well as hop-by-hop migration request propagation. Extensive simulation experiments show that RMBCC can be efficiently integrated with different on-path caching strategies. Compared with representative caching schemes, RMBCC achieves significant improvements in evaluation metrics such as cache hit ratio and content retrieval time, while only introducing negligible cooperation overhead.