We have an Automation rule in place that assigns a user to an Organization based on their email address, like so:

This works without issue for registered users. However, we'd also like to be able to assign anonymous users (those who have submitted a support request via email without creating an account) to an Organization.
Is this possible?
Our ultimate goal is to be able to view support tickets grouped by Organization, as we have different agreements depending on the customer's real-world Organization, so therefore seeing all tickets made by customers from X organization in one area, and Y organization in another, is desired.
We can't force users to create an account, because an agreement we have with one customer organization is email support.
So I guess my wider question is: Is there any other way to group support requests submitted by both registered and anonymous users, based on their email address domain?
Thanks!