In the general case (a form with subordinate forms), you’re looking for the formsets.
In the more specific case (subordinate forms based on a one-to-many relationship), you’re looking for model formsets.
You can certainly build Class-based views for working with these. However, most people find that trying to use formsets with the Django-provided generic editing views to be a bit frustrating. Those views really are designed around the idea of editing a single instance of one model. Formsets tend not to be a good “fit” for them.
When we use formsets, it’s either with an FBV or with a view directly inheriting from View.
(Also, you might want to search this site for “formsets”. There have been a lot of previous discussions here about them.)