Beyond the Beyond (ɮ)

Define ɮ as the smallest possible ordinal that when plugged into any given ordinal mapping hierarchy to any given "n<100" would produce a result bigger than the $$f_{BN}(n)$$th ordinal-based function applied to $$f_{BN}(n)$$ in $$f_{BN}(n)$$ systems of ordinal-based functions.

Beyond the Beyond = $$f_{ɮ}(n)$$th