Django: Adding an intermediate model to a ManyToMany field without one

Django’s Many to Many relationships allow you to have a many-to-many relationship without an intermediate model — this is great for when you don’t need anything except foreign keys on the through table, and gives you an easy API to work with to get related objects. But what about when business needs change, and now you do need additional fields on the intermediate model — and you need to make the change without any downtime or loss of data?