How do I let all contacts within an organization see and edit all incidents for the organization?

Summary:

Hello, I've been looking around in the documentation and searching online and haven't found a way to allow the contacts in the same organization to all have access to and update the organization's incidents. How is this done?

Content (required):

I have a situation where we frequently encounter one contact for an organization submitting an incident, then another contact from the same organization wants to update that same incident. We currently have to get a phone call from the organization requesting that we switch the contact manually for the incident. Is there a way to allow an organization to manage who its contacts are for each incident itself?