This sounds a little tricky. My best guess would be to have an application structure such that the modal is attached to the topmost view. With some clever CSS and JavaScript, you should be able to make the modal float at the press of a button so that the user can continue navigating other parts of the application.
Your application.hbs should be roughly something like
<modal></modal>
{{outlet}}
so that the modal always exists alongside all of the other application views/routes.
If you have a button in one template that needs to talk to the application controller/route/component, apparently it’s possible to do this based on this post assuming that I am understanding everything correctly.