Update: above is a picture of the "opgang" I lived in, in 2001 in Copenhagen.
In Danish, a set of apartments connected to the same stairwell is called an "opgang". But what's the English (or American) word for it?
OK, you have a street with many apartments. No space between the houses. And each door leads into a stairwell with, say, six apartments. "Opgang" is used both for the stairwell itself (the word means "walk-up") and the whole set of apartments connected to it.
Maybe this arrangement of apartments, so exceedingly common in Copenhagen, is not very common on a global scale.
I don't think there's a word for it. But it would be very useful for city dwellers. A guy today called it a "unit". Like:
"I spoke to somebody from your unit yesterday, they said you got a new back door."
"When we moved in, we held a housewarming party for everybody in the unit, to get to know them."
"I've lived here for two months, and I still haven't met everybody in the unit."
I've also heard it called a "block". Though that's also used for all the houses between four streets.