Como dizer ''O prédio tem muitos andares" em inglês

"There are too many storeys in this building"

In general, to state "high rise apartment buildings", "towers" or something like this, would convey the idea of having many floors.
It seems like "storeys" is more used in the UK in the sense of floor (or almost in that sense, that is, 'storey' is in the sense of the level of a building).

In the US floor is more used (in that sense of 'floor structure' of a building) and a storey would be a measure of the height (of the building, here).
A high-rise would be defined as a higher than 75 feet (23 meters) - OR, if you wish, an 8-floor building.

Anyway, sometimes they announce 'story' meaning the same as 'floor' (even in the States) like they did with Metropolis, a "56-story luxury skyscraper/tower" in LA. And some other skyscrapers might have even 100 floors!

Anyway, a "multi-storey building" (OR multi-story building, if you wish) would mean a building with many floors (five or more), a high-rise would mean 12 floors onwards. It's a fixed expression to speak of tall building (hence with lots of floors).

Recomendo:

It's a multi-story building. [O prédio tem muitos andares.]

Bons estudos.