I used to live on the 7th floor in a building on Congress St, which is in downtown Portland. Whenever I told a local that I lived on the 7th floor, they commonly responded with confusion, and said, "There's a building in Portland with that many floors?"
They were being facetious, since there are probably oh, hmmm...... maybe 9 or 10 buildings downtown taller than 4 stories. Most of the taller buildings are headquarters for the different banks, NBC, some law firm, and two "city center" buildings with businesses in them. I'm not sure if they have apts or if they do, how to go about finding them. I wouldn't recommend the building that I lived in.
The previous poster is right - in Bidd, Saco, Kennebunk, etc. you won't find a building taller than 3-4 stories.
One place that seems to own alot of the downtown apartments is called "Apartment Mart". I know, it's a K-mart, ghetto sounding name, but they really do have hundreds of apartments that they lease and might be able to help you find something. Their number is 207-773-1814. Another tall building that might have high-rise apts is called back bay towers. 207 772 7050. probably 15-20 stories high, which is tall for Portland. I always thought it was an assisted living place, but I'm probably wrong. I've never been there. Anyway, good luck to all looking for housing.
Unfortunately, although there are 120 students in each class, you probably won't find any one particular building/complex where more than 6-7 students live. Alot of students live on Hills beach or Biddeford Pool in the seasonal rentals, so it is possible to at least live within a couple of blocks of a large number of classmates.