階位 is read as かいい (kaii) and means rank.
かいい
kaii
いかい
court rank
かんいじゅうにかい
first system to rank officials into 12 levels (603 CE)
いかいくんとう
court rank and honors
かい
counter for storeys and floors of a building
かいだん
stairs
しな
quality
かいそう
class
かいか
bottom of the stairs
かいじょう
top of the stairs
かいだか
height of a storey
かいちょう
gradation
かいすう
number of stairs or stories (storeys)