Add field to many-to-many relationship

Relationships do not have fields, so to achieve this outcome is to create a "junction" style module.

For example, lets say you have a custom module (Events) and your core module (Contacts). You want to be able to say that many people attend many events and track some information about that relationship (e.g. are they invited / attending etc).

Instead of creating a m:m relationship between the two modules, create a new custom module "Event Registrations", with a 1:m relationship each way, i.e. one Event has many Event Registrations and one Contact has many Event Registrations. Then at the Event Registration level, you add the fields - e.g. status, dietary needs and anything else which you would have otherwise considered a field of the 'relationship'.

You should be apply this same approach to your implementation with your Cases module and the custom module.

Thank you Adam, I was able to produce the functionality you were describing. 

Agreed. This type of 'in-between' module can be very useful when using fields that describe what that relationship between the two outer modules is. We often add some auto naming rules for this 'in-between' module