Converting a back terrace into a second bedroom

We live on the third floor of a brownstone with an extension. The roof of the extension is our terrace, which we access from our living room. My question is, and I know it sounds crazy, could we close up this terrace and turn it into another bedroom? Maybe convert it into a sunroom or something like that? The terrace is on the back of the building so it’s not visible from the street, it is aprox 200 sq ft.