When I was living in Edinburgh, I encountered the corner case of the upper levels of an apartment building having a different postcode from the lower levels.
Everything online used the same address database so I wondered why I could never find my address under my (presumed) postcode.
When I worked at Scottish Gas, dealing with tenement flats in Edinburgh was always a nightmare because TGB (the old billing system) used the old 1F/2F/3F system but the electricity system used the numbered system - so customers would get mail for both but it would be mixed up all the time.
If you have to deal with a pre-pay meter going in, or just a change in meter they usually screwed up the MPR number with the address and end up replacing the wrong one.
And I lived in Edinburgh for 13 years, mostly in tenement flats - so it was always a hassle.
Edinburgh is awesome, in particular, for the way that flats can be numbered within buildings.
I used to live in flat on the top floor which received mail as either "TFL" (for top-floor, flat on the left", or "Flat 6". Different companies used different formats for the address.
I'd lived in GFL "ground-floor, flat left" and "GFR" for "Ground-floor, flat-right" as well. But never in a middle floor. I assume they would be MFL and MFR respectively. But who knows?
Flats on floors in between usually have the floor number as the first part: "3FL" for third floor on the left or "2F3" for second floor, third flat. Or at least that's how it was when I lived in Edinburgh in the 90s.
Here's a recent reddit thread on the problems of post and delivery services, and the address format for tenements. It discusses 'royal mail' vs 'council format' and the PAF
when i lived in edinburgh in the 70s, we would just stick a card on the flat door with the surnames of the inhabitants on it - the flats themselves did not have numbers.
Norwegian apartments are all identified by a single letter and four numbers. For example, H0203 means 2nd floor, 3rd apartment from the left as seen when ascending the stairs. The H means "main floors" (as opposed to the loft or cellar). Very useful when visiting other apartments.
I've seen this done (in England) for blocks of flats where each floor has it's own postcode that matches the floor, eg ZZ1 Z1A through to ZZ1 Z1G (A-G for floor 1 to 7).