I think that an example of a cognitive-developmental approach can be found in the following book: How we interpret art: A cognitive developmental account of aesthetic experience, Parsons, M. (1987) Cambridge: Cambridge University Press. In this book Parsons identifies 5 stages in one's understanding of art. Therefore, this book is a good example of a cognitive developmental approach applied to human artifacts, namely to the beautiful domain. Note that it is often the case that cognitive-developmental approaches have been applied to the cognitive domain (e.g., Piaget's theory) and the moral domain (e.g., Kohlberg's theory).
Best regards and good luck for your interesting project
Thank you for your suggestions! This is exactly the kind of book I am looking for. In this case, I have read it already and I referred to it in my working notes. I also agree about your differentiation of specific domains like the beautiful or aesthetic, the cognitive, and the moral. In this regard, I find Habermas's formal pragmatics very useful.