If you rent a place you shouldn't change the exterior (Unless you are trying to restore it to how the apartment should look after it was griefed by the previous renter. Renting a place after modifications has been made by the previous renter doesn't justify the changes, they should be fixed as soon as possible.). This included changing exterior walls to add windows, change the block types, or adding onto the apartment. As this can degrade the exterior quality of the building. Especially because most apartments are part of larger structures or groups of apartments and changing one destroys the synchronous nature of these structures.
If you own the apartment building, you should not add on to the building if it would make the building look less impressive as it was or if it would impact the buildings ability to keep up with city standards. For example, you can't just make buildings taller and taller infinitely. Buildings have to be proportionate and realistic on Cities, and therefore they have to be built modestly. And even if the building would be proportionate adding on, you have to consider the area of the city your building is in and keep your building reasonably similar to the others. This applies to size and design of the building. In most cases, you should not add onto buildings because most plots are designed at the height they should be at. If you need more space in your owned plot, I would suggest building down and adding basement space because then you can add many more floors without affecting the look of the area your plot is in and risking a city standards violation.
So, without knowing the specific plot you're asking about, I hope this helps!
I used to spend ages trying to fix apt grief when I was an admin, this stuff is really common on Cities. xD