Homes come in a lot of shapes and sizes though - in Italy where I lived for a number of years, it's pretty common for people to live in a flat in a 4/6/8/whatever unit building, either as owners or renters.
Depending on where demand is, I'd expect more of that sort of thing too, if it's allowed. In the US, it is forbidden to build those kinds of homes in large areas of our cities.
Here is the graph for multistorey apartment buildings. I'm not smart enough to interpret what this means. In the big city I live in in Denmark, most new apartment buildings are luxury apartments and expensive as hell, so I don't think they are a result of rising house prices.
https://i.imgur.com/wF6PCnU.png
2019 is not over yet, so maybe it's a little higher this year.
This is only for "parcelhuse", which wikipedia defines as: "Single-family detached home".