User blog comment:Edwin Shade/You Know You're a Googologist When.../@comment-11227630-20171014160901/@comment-32876686-20171014175605

There is a blog post here by Deedlit11 which has a letter by Keith Ramsay in it that goes into what you're asking.

Googology level 4 would seem to be languages to describe languages, but this still uses languages, so you can't really call it a larger new sort of concept. I'm not sure what would come next.