Emerging industrial applications such as factory automation with automated guided vehicles often require time-sensitive communication across multiple domains. Although these scenarios may have independent operating domains, the global traffic still needs to meet end-to-end latency and reliability requirements. This complicates scheduling in multi-domain Time-Sensitive Networking (TSN). Current approaches often rely on a global orchestrator that computes a single schedule for all streams. These centralized solutions are computationally demanding and undermine the separation of concerns between domains. Additionally, the large number of individual streams makes scheduling infeasible without aggregation mechanisms. To address these challenges, we propose a system model for multi-domain TSNs with domain-specific controllers. Inter-domain streams are assigned to service classes that combine aggregation with constraints inspired by frame-based scheduling, which capture additional delays at domain borders. Within each domain, the service classes and intra-domain streams are then scheduled independently, distributing the global problem into smaller subproblems. Our evaluation compared to a globally scheduled TSN shows that multi-domain scheduling achieves comparable end-to-end latency guarantees, while improving scheduling runtime performance by a factor of up to x20 and lowering a part of the device state by up to 40 % through stream aggregation. Domain borders introduce additional delays that can be controlled systematically through our proposed constraints combined with the service class assignment. Our work demonstrates the feasibility of scalable and reliable inter-domain scheduling without a centralized orchestrator, contributing to the development of future industrial TSN networks in which wired and wireless domains coexist.