uncountably

As a noun taxonomy

is the science or the technique used to make a classification.

As an adverb uncountably is

too many to be counted (either by reason of being infinite or for practical constraints).

As adverbs the difference between uncountably and numberlessly

is that uncountably is too many to be counted (either by reason of being infinite or for practical constraints) while numberlessly is in a numberless way; uncountably, infinitely.