From Wiktionary, the free dictionary
From sub- + basement.
subbasement (plural subbasements)
- A basement located beneath another basement
2007 February 8, David W. Dunlap, “What May Have Made Good Neighbors Now Present a Puzzle”, in New York Times[1]:Joan H. Geismar is trying to unravel the mystery of old stone walls in the subbasement of Federal Hall National Memorial on Wall Street.