multi-storied pagoda; many-tiered tower
Refers to a pagoda with multiple tiers, typically in Buddhist temple architecture. The term is technical but understandable.
There are several beautiful multi-storied pagodas at temples in Kyoto.
This multi-storied pagoda is a five-tiered tower and is designated as an Important Cultural Property.
Compound of 多重 (multiple layers) + 塔 (tower/pagoda). The exact historical derivation is straightforward.