According to @RalphJ's first comment on my earlier question about ILS approaches in an E-Jet sans pitch trim:
Are you sure that Cat III approaches are allowed in that condition? Typically, Cat III requires basically everything to be operative, unless there is some pretty unusual redundancy in the aircraft. Wouldn't be surprised if one channel out removes Cat III, and then losing the 2nd channel takes out Cat II. Just a guess, but the list of things required for Cat II that aren't needed for Cat III, while not empty, isn't very long in most cases. [Emphasis (both bolding and italics) in first sentence present in original; emphasis in second and last sentences mine.]
"Requires basically everything to be operative" seems like basically the highest bar possible in terms of functional functionality, so that's kinda difficult to square with it being possible for something to not be required for an ILS-III approach despite being required for an ILS-II approach.
What sort of things would an aircraft require to be operative for an ILS-II approach, yet not need in working order for the more-demanding ILS-III approach?