階 (Kanji for story of a building)

Onyomi

KAI	You heard the one about the crazy lady flying her KITE from the 8th story window.

Everyone in the whole town lives on the same story! The whole rest of the building is vacant.

階段(かいだん)	stairway ★★★★★ 階 (story of a building) + 段 (step / stairs) = 階段 (stairway)
ｘｘｘ階(かい)	story ★★★★★ COUNTER story of a building. いっかい、にかい、さんかい。。。
段階(だんかい)	step/phase ★★☆☆☆ 段 (step / stairs) + 階 (story of a building) = 段階 (step/phase) a step in a process. A measure, as in "We're taking steps to reduce your mother's underarm emanations." Also a palindrome of stairway!
階級(かいきゅう)	social class ★☆☆☆☆ NP 階 (story of a building) + 級 (level) = 階級 (social class) a rank, grade, class.(usually used in the sense of social class)