And did something absolutely stupid! I defined a thing.
It's the "dipsi" function, Ψψ(n). Simply put, Ψψ(n) is the largest number definable within n standard universes, assuming a "standard universe" has a volume the same as the observable universe, and each symbol takes up 1 planck cube of volume. Note that it is different from RAYO(n * 9.475 * 10^184). Note that this excludes dipsi and higher variants (and anything defined by it or its higher variants), but not anything else similar, like RAYO(n). RAYO(n) and similar are fair game.
But dipsi is beaten by tripsi, which is defined as dipsi nested n times, with n being the n of the innermost dipsi; it's Ψψψ(n). Ψψψ(2) is... decent, to say the least, being Ψψ(Ψψ(2)).
Nesting tripsi the same way gives quadrupsi, with pretty much the same definition, but with "dipsi" replaced with "tripsi". It's Ψψψψ(n). Similar rules, but it can lead to surprisingly deep nesting.
Of course, there's a reason why the name of the google doc I did this on in ~10 minutes has "naive" in the title. These are likely deceptively weaker than intuition would expect, although at least a tiny smidgen more powerful than RAYO(n). I could easily extend this further than quadrupsi, of course.