Multi-server Federated Learning (FL) has emerged as a promising solution to mitigate communication bottlenecks of single-server FL. We focus on a typical multi-server FL architecture, where the regions covered by different edge servers (ESs) may overlap. A key observation of this architecture is that clients located in the overlapping areas can access edge models from multiple ESs. Building on this insight, we propose FedOC (Federated learning with Overlapping Clients), a novel framework designed to fully exploit the potential of these overlapping clients. In FedOC, overlapping clients could serve dual roles: (1) as Relay Overlapping Clients (ROCs), they forward edge models between neighboring ESs in real time to facilitate model sharing among different ESs; and (2) as Normal Overlapping Clients (NOCs), they dynamically select their initial model for local training based on the edge model delivery time, which enables indirect data fusion among different regions of ESs. The overall FedOC workflow proceeds as follows: in every round, each client trains local model based on the earliest received edge model and transmits to the respective ESs for model aggregation. Then each ES transmits the aggregated edge model to neighboring ESs through ROC relaying. Upon receiving the relayed models, each ES performs a second aggregation and subsequently broadcasts the updated model to covered clients. The existence of ROCs enables the model of each ES to be disseminated to the other ESs in a decentralized manner, which indirectly achieves intercell model and speeding up the training process, making it well-suited for latency-sensitive edge environments. Extensive experimental results show remarkable performance gains of our scheme compared to existing methods.