User blog:Hyp cos/Googolisms hard to extend?

Here, to extend a googolism (large number) means to make a larger number in a similar way.

Some googolisms from "notations" such as array notations, hydras, FGH/HH/SGH + OCF, are easy to extend. For instance, Bird's \(U^{U(3)}(3)\) can extend to a new part of Bird's array notation, with arrays as subscript of the slash. Extending to large branches of new numbers is not much more difficult than understanding the notation itself.

Some googolisms resulting from "combinatorial functions" are also easy to extend, though naive extension. For instance, from TREE(3) there are simply TREE(4), TREE(5), etc.

But there are still some numbers appearing singly, or even without any "input parameters", thus hard to extend. A cool example is 808017424794512875886459904961710757005754368000000000, which can be defined as "the largest order of finite simple groups that are not cyclic, alternative, or of 16 families of group of Lie type".

Are there another googolism of this kind, i.e. hard to extend?