Aggregation relationships to multiple parents

Summary

Is it possible to have more than one parent with aggregation relatiionships to the same child?

Content

Hello,

A technique often recommended in the community for setting up many to many relationships is to create a cross reference custom object.  When this occurs, say between the contacts object and the organizations object, when a contact is deleted, its relationships to the organizations should also be deleted.  And when an organization is deleted, its relationships to contacts should be deleted.  It is my understanding that for this to happen automatically, both relationships to the cross reference table would need to be an aggregation relationship.  Is this acceptable?  And will it work as I described?