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You need to build your own permission system.
Django’s built-in permission system is not suited for what you want to do.
Build models for the Project. Create a ManyToMany relationship between a User and a Project through a Membership model. This Membership model will have a role field.
https://docs.djangoproject.com/en/1.10/topics/db/models/#extra-fields-on-many-to-many-relationships has an example that is almost ideally suited for your needs.
You can not do user.has_perm('edit_project', project) in a template. Django templates do not allow function calls directly with multiple params. I think in your case a custom template tag that takes a User instance, a Project instance, and a string describing the desired permission would be the way to go.
