Intermediary Object : adding extra fields for smart list definition usage

I am currently investigating if it is possible to add extra fields to an intermediary field ( custom objects ) that can be used in a smart list definition.

For example, I have a Custom object of products, and my intermediary object is the link between a contact and a product purchase.

I have added a field to the intermediary object : purchase date.

My smart list is based on "added to product", by I want to refine it with for example after a certain purchase date.

Problem is that I can only see the fields of the product custom object in my smart list definition, and not the extra fields from the intermediary object.

Can someone tell me how this can be solved?