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.
"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].
<a href="https://www.etymonline.com/word/multistory">Etymology of multistory by etymonline</a>
Harper, D. (n.d.). Etymology of multistory. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/multistory