Multiprocessor Systems-on-Chip (MPSoC) applications can rely today on a very large spectrum of interconnection topologies potentially meeting given communication requirements, determining various trade-offs between cost and performance. Building interconnects that enable concurrent communication tasks introduces decisive opportunities for reducing the overall communication latency. This work identifies three levels of parallelism at the interconnect level: global parallelism across different independent domains; local or intradomain parallelism, relying on inherently concurrent interconnect components such as crossbars; and interdomain parallelism, where multiple concurrent paths across different local domains are exploited. We propose an automated methodology to search the design space, aimed at maximizing the exploitation of these forms of parallelism. The approach also takes into consideration possible dependencies between communication tasks, which further constrains the design space, making the identification of a feasible solution more challenging. By jointly solving a scheduling and interconnect synthesis problem, the methodology turns the description of the application communication requirements, including data dependencies, into an on-chip synthesizable interconnection structure along with a communication schedule satisfying given area constraints. The article thoroughly describes the formalisms and the methodology used to derive such optimized heterogeneous topologies. It also discusses some case studies emphasizing the impact of the proposed approach and highlighting the essential differences with a few other solutions presented in the technical literature.