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Douglas Harper's Etymology Dictionary
multistory

also multi-story, multi-storey, 1918, from multi- + story (2).

Wiktionary
multistory

a. (alternative form of multi-storey English)

WordNet
multistory

adj. having more than one story [syn: multistorey, multistoried]

Usage examples of "multistory".

How many times had I stood across the street from this multistory compound, staring up like a lovestruck boy and waiting until the lights were lit in the upper apartments and terraces, hoping against hope for just a glimpse of the woman?

The third and fourth blocks ran along one side of the Morningside Project, a multistory housing development and a major source of the students she would be working with.