The second floor of Hogwarts is the location several bathrooms, including the girls’ bathroom haunted by Moaning Myrtle. The Defense Against the Dark Arts teacher’s office is also located on the second floor (although Umbridge’s office was on the third floor, not the second (OP13)). A map of Argyllshire hangs on the wall there (PA9). A shortcut behind a tapestry on the second floor leads to Gryffindor Tower (HBP14), which is likely the same one which ascends two floors by way of a narrow staircase with a trick step (GF25). During the downfall of Umbridge after the Weasley twins left Hogwarts, Peeves flooded the second floor by removing all the taps in the bathrooms (OP30).
Although the marble staircase only extends to the first floor, there is another flight of stairs close by which leads up to the second floor. When students leave the Great Hall and head for their common rooms, they go up by way of these two staircases to the second floor. For some reason, the Slytherins also seem to take this route, although their common room is in the dungeons, since Draco is among the students who confront Harry, Hermione, and Ron after the Halloween feast (CS8, CS9).