In that discomfort, breathing quicklime and tar, no one could see very well how from the bowels of the earth there was rising not only the largest house in the town, but the most hospitable and cool house that had ever existed in the region of the swamp.
(One Hundred Years of Solitude, tr. by Gregory Rabassa)
The that-clause is a complement providing the criterion for ‘the largest’ and ‘the most’, isn’t it? (It seems like the ‘indirect complement’ that is said in ‘The Cambridge Grammar of the English Language.')