full two-story house
Refers to a house where the entire ground floor footprint is built up to a full second story, as opposed to a partial second floor. Used in real estate and architectural contexts.
This property is a full two-story house, so the second floor is also spacious.
Compound of 総 (そう, 'whole, entire') and 二階 (にかい, 'second floor'). The exact historical derivation is uncertain, but the term is conventionally used in Japanese architecture to describe a full two-story structure.