Having several stories: a multistory hotel. (adjective)
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Use "multistory" in a sentence
"Each firefighter — wearing 50 pounds of gear, including an air pack — starts with an additional 45-pound hose pack (sometimes called an "apartment pack" or "hotel pack," a set of preconnected hoses used to fight fires in multistory hotels and apartments) on his shoulder and has to run up 63 steps to the top of a five-story tower."
"A multistory building that guards said served as Gadhafi's library and office was turned into a pile of twisted metal and broken concrete slabs."
"Other more recent projects by Gwathmey Siegel, which employs 25 architects, include the 22-story United States Mission to the United Nations; the Setai Fifth Avenue, which is opening next month; and a multistory residential project, Soho Mews."