You are correct that this is a limitation of the current version's user interface - the data model actually supports the type of many-to-many relationship you describe.
A work-around for this version is for Individual Providers who are affiliated with multiple Organization Providers to not track their affiliations at this point, but rather to use the support for multiple "Locations" to track the affiliation. You can also use the notes to track the roles they perform at the different Organizations they are associated with.
Thank you for bringing this issue to our attention - we will attempt to improve on the user interface for future releases.
Support Team