Service Desk already has the concept of global front end. If I go example.com/servicedesk/customer/portals, I can access all the customer portals from there by project.

Additionally, there should be a feature to enable a global service desk backend. This should exist for the purpose of teams that support multiple products so that they will not have to either jump across queues from project to project or have to resort to creating queries and sharing around an issue filter.