How to link two Organizations with a pair relationship?

I have this situation I’m working on since way too long involving a sub type of Organization.

I work for a professional Union and 2 sub-organisations can belong to the same person. Which means that one contact owns 2 organizations or said differently two organizations share the same organization contact.

My first approach was to create an individual contact and an organization with a relationship of type owns/is owned by. Using the same individual contact, you could register dozens of organizations with this vertical link. The thing is that for my processes, all memberships acquired by the organization level were transferred to the individual and I couldn’t have receipts for each particular organization with the specific contribution and the name of the owner (even with extended tokens)

So now, I changed my mind and focus on the relationship between organization. I’ve created a pair relationship and I’m wondering about how to link organizations between them. I thought about a CiviRule that would compare the custom fields created for the contact within the organization and add the relationship type (but haven’t succeeded yet). I also thought about prepopulating custom fields from the URL sent after the first registration.

How would you deal with that?

(I’m working on Drupal 7.72 and CiviCRM 5.25 using a webform for the registration)