Many Googological functions are based on up-arrow notation and
related concepts, which stems from using exponents. But wouldn't it
be possible to use the same systems with a more powerful base
function, even an uncomputably powerful one? For example, you can
define a function that is equivalent of up-arrow notation, but for
FOOT.

LEG{1}(a, b) = FOOT^b(a)

LEG{n}(a, b) = FOOT^(LEG{n-1}(a, b-1)) (a)

Then, equivalents of functions based in up-arrow notation can be
defined using LEG, and so on.

Hyperrecursion of uncomputable functions seems like a pretty
powerful thing.

They say great X is built on the shoulders of giants. That
includes big numbers, and Meameamealokkapoowa oompa qualifies. So
of course I had to start by making Meameamealokkapoowa oompa
loompa, the obvious first step. Then I came up with an idea that
would be much bigger and harder to solve, forming Gigoombaverse.
Then I turned that into a function. But now I have a new idea,
which will have many repeats and be very recursive and very big.
(as in Gigoombaverse ~= 1 big).So beware!!!!!!