It seems that since the 1980s we have been looking for the answer to the question, what comes after postmodernism. The most recently published effort in this direction is an impressive book by Jason Ananda Josephson Storm, a religious studies professor, titled Metamodernism: The Future of Theory. The University of Chicago Press, 2021. I very much enjoyed reading this challenging book which I originally ordered because of my ongoing interest in Weitz's anti-essentialism. Storm shows a great deal of wisdom about ongoing debates both in philosophy and in the social sciences. However, as with all other writers on the topic, he missed Weitz's main point and principle discovery, namely that the history of defining art is a history of successes, not failures, as long as we take the proposed real definitions to actually be honorific re-definitions. Unlike Weitz I hold these honorific re-definitions to be descriptions/constitutions of the emerging and always changing essences they define. So my solution to this classical problem mediates between essentialism and anti-essentialism. Storm rightly sees that we cannot stick with traditional essentialism and hence cannot define such key terms as "religion" and "art" in terms of necessary and sufficient conditions. He also raises excellent objections to the family-resemblance approach (which he wrongly, along with everyone else, attributes to Weitz). However he believes that the solution to the "legitimation crisis" of our time is a "process social ontology" which replaces the idea of "natural kinds" with that of "social kinds." He believes that this gets beyond anti-essentialism. He sees social kinds a "homeostatic property-cluster kinds" and a similar approach has been followed in aesthetics. However, this approach drains any discussion of essentially contested concepts of their dynamic energy. We just end of up with what was once called "descriptive metaphysics." Dialectic is lost.
Some of the things that he says about social kinds do capture what I mean by "essences." But they miss the Socratic question and the Socratic quest which I take to be foundational of philosophy and the paradigmatic philosophy language-game. Such theories are merely descriptive and do not recognize the ideal aspect of essences. As I have said (although mainly in unpublished writing), the ideal aspect is empty in content but is eternal and unchanging. One might say that the "social kind approach" to essences fails to see and deal with the ladder of love in Diotima’s sense. In doing so, it fails to capture the best of idealism. On my view, the essences (of social kinds) are emergent from the dialectic between the ideal aspect of essences and the processual social kind. Without this dynamic there is no possibility of creativity in the analysis of, and constitution of essences. I worked out my views on this way back in the 90s in - “The Socratic Quest in Art and Philosophy,” The Journal of Aesthetics and Art Criticism 51:3 (1993) 399-410. and “Metaphor and Metaphysics,” Metaphor and Symbolic Activity (Special Issue on Metaphor and Philosophy) 10:3 (1995) 205-222.
I do like the term "metamodernism" and I would say that metamodernism is the answer, but not Storm's version.