How do you change the template for a shared section?

Perch 3.1.5 I know how to change templates for sections that are just on one page by deleting that section from the list on the page refreshing and selecting a new template. If the template is shared across many pages how does that work. If you delete the section from shared won't that mess things up? How is that done so it still works across all pages because that section does not show up on the pages individually.