[yters]

But then you can have an even more powerful BB that has access to a halting oracle. Then you can have the oracle hierarchy. And then maybe there is another meta direction on top of that.

It seems there is no limit to metaness, and that unlimited nature cannot be captured by notation, otherwise one can go meta on whatever notation is used.

It is like the corollary to "there is no highest number," there is also no fastest growing function. Whatever function one names, it is always possible to use that function to define an even faster growing function.