How can we implement company-wide releases?

[Colin Scott]

My organization has a number of systems that each have their own release schedules. We have hundreds of one-off projects that are running simultaneously, and each project has stories that may be associated with these systems and their release schedules.

Is there a way we can have releases span the entire company instance, so when the release for a system happens, it is applied to all stories associated with that system's release? This would also mean that a defect caused by a project can be placed in that project (because it will be fixed by that team), but would abide by the associated system's release schedule.

I've looked at Portfolio for Jira for cross-project releases, but that would add a significant amount of complexity since every project would need to be in one plan. Someone from Atlassian recommended utilizing Programs, but those are only available in Jira Server. Is anyone else in a similar situation? How do you manage your release schedules with system-specific releases and one-off, cross-system projects?