also multi-story, multi-storey, "of many stories or floors," 1907, from multi- "many" + story (n.2).
Entries linking to multistory
multi-
before vowels mult-, word-forming element meaning "many, many times, much," from combining form of Latin multus "much, many," from PIE *ml-to-, from root *mel- (2) "strong, great, numerous." It was much-used in forming Latin compounds in classical times and after (such as multianimis "having much courage," multibibus "much-drinking," multicomus "having much hair," multiloquus "talkative"). Many English words that use it (multinational, etc.) are 20c. coinages.
story n.2
"floor of a building," c. 1400, from Anglo-Latin historia "floor of a building" (c. 1200), also "picture," from Latin historia (see history). "Perhaps so called because the front of buildings in the Middle Ages often were decorated with rows of painted windows" [Barnhart].