Yes you can! The whole back yard is designated as a public area. In a public area, you don't own anything (which is why it's so cheap with 3 arcade games, 3 high end washers, 3 high end dryers, a hot tub and a full playground), so you can't alter it at all unless you put the cheat codes in. Likewise, when you move, you can't take any of that stuff with you, even if you "pack furniture." But other than that, you can do whatever you want in it.
One thing I noticed about Bridgeport is that if you had any intention on raising a family, you weren't going to be doing it comfortably in an apartment. There
is one really good one, but it starts out occupied by the "Art Central" crew. There are some larger, more expensive apartments available, but they're all 1 bedroom, and even with the expansive size, when your family grows from 2 to 3, things start getting cramped.
This was an experiment for the most part. I wanted to see if it was possible to make a family oriented apartment, and to see how much it would cost in the end. And it was a
lot cheaper than I expected it to be. I went bare minimum on the furnishings, but I could upgrade a lot of the appliances and the furniture and it would
still be affordable by a single sim fresh out of CAS. But most of all, I wanted to familiarize myself with the process. And I learned something very important: once you actually try and do it, you find out it's easy as pie. Really, anybody who has ever built a house and has even a minimal knowledge on using cheats could do it. It's literally
that easy.
While I was just messing around, I actually made a very workable apartment. Plus, it gave me dozens of ideas for my next one.
Also, I was careful not to use anything that didn't come from the base game or the 3 expansion packs (no store downloads or stuff pack items), and it was done on a 40x30 lot. The landscaping is terrible, but if anyone wants it, I'll upload it to the exchange or submit it to the swap shop. And you don't even have to feel guilty about altering it.