Objective: The explosive growth in the number of beams and overall bandwidth requirements in broadband communication satellites has made onboard hybrid optical and electrical switching a critical technology for supporting large-scale and low-complexity switching systems. However, the design of scaling optical switching using Clos networks, onboard hybrid optical and electrical switching, which is based on the decoupled design method, currently disregards the coordination among various switching parts. This decoupled method results in redundant switching paths, inefficient mapping, and substantial increases in the number of optical switching units and interconnecting optical fibers. These inefficiencies cause inconvenience in the limited onboard transponder resources and hinder the scalability of future satellite systems. Methods: To address this issue, this study proposes a joint design method that combines expansion and merging. Firstly, the optical switching scale is expanded to meet the overall functional requirements, and the optical switching functions of down- and up-conversion parts are merged and executed in the down-conversion part, thereby reducing the number of optical switching mappings. This expansion results in the formation of a unified switching domain that increases flexibility in resource allocation and lays the foundation for merging. Secondly, the Clos network topology is used as a basis to achieve a part of the optical switching functionality through the reuse of electrical switching capabilities. This functional reuse enables the effective merging of optical switching modules, which reduces redundancy and minimizes intermodule communication overhead. Results: The analysis indicates that the number of optical switching units is reduced by 9.5% to 50% without increasing the scheduling complexity. The number of corresponding interconnecting optical fibers is reduced by between 1/8 and 3/8. Furthermore, the channel scale varies in response to demand changes, with a typical scenario involving the selection of half of the total broadband channels for fine-grained electrical switching. The effectiveness of the proposed methods is demonstrated in various cases under the corresponding scenarios. When the total number of channels is 84, the optical switching modules attain a reduction ratio of 50%, whereas that of interconnection fibers is 1/4. Moreover, the proportion of fine-grained switching in the total switching scale consistently varies based on the changes in demand. For specific cases, at a fine-grained switching ratio below 0.6, a considerable reduction in optical switching modules occurs, which highlights the effectiveness of the proposed method. Finally, the scheduling complexity introduced by the joint design is analyzed. Although the design introduces additional swap operations at the input and output channel levels during electrical switching, such operations cause no increase in the time complexity of the optical switching scheduling algorithm. Thus, the joint design maintains computational efficiency similar to that of traditional methods while achieving substantial improvements in physical resource savings. Conclusions: The proposed joint optimization method based on expansion and merging offers an effective and scalable solution for hybrid optical and electrical switching in broadband satellite communication systems. Through enhanced coordination across various switching parts and optimization of the utilization of optical and electrical resources, this method effectively addresses the challenges encountered in scaling Clos networks in onboard environments. Thus, it holds crucial promise in enabling future satellite networks that require high capacity, low complexity, and great flexibility in switching architecture design.