Eh. That is still not a common word or theory. I think it is contrived.
A lot of modern philosophies are already self-referential metatheories. So the label for philosophy-of-philosophy may just be unproductive.
Historically, we tend to split the self-reference the other direction: vertically instead of horizontally.
- 20th-century analytic philosophy is wrapped around the logic of logic in the form of metamathematics,
- Nietzsche's 'beyond good and evil' ethics is an ethics-of-ethics question,
- postmodernism is a narrative about our narratives about narratives,
- existentialism is largely a rational psychology of rational psychologies addressing why we bother to explain anything.
So people are already doing meta-analysis, meta-ethics, meta-semiotics, meta-psychology... and they don't seem to feel that takes them out of their own branch of philosophy, much less into some separate place named meta-philosophy. It is awkward to snip out just the recursive parts of a given vertical, so we would have a hard time populating meta-philosophy that way. The result would not be a discipline, just a filter.
What is left would we whole philosophies, in the systematic sense of Aristotle, Kant, Spinoza etc. that are themselves recursive, and include other philosophies in their model of the world in an explicit way. That would be an insane demand, as it would require an ethics that applies to semiotics as well as ontology, a psychology that applies epistemology and ethics...
Labeling something does not make it happen, and choosing for your perspective to have a specific intention does not make it work. This is a term destined for the dustbin, for while it identifies a phenomenon, as a field of inquiry the result is either artificial, disconnected and disjointed; or it is empty.