I can't answer you with certainty, but from the layout of the app, a second station would probably be of no use to you. Even if you had a second charging station, the robot would only recognise one station. But you don't really need a second station. We also have two floors. Simply carry the robot to the second floor and start it. It automatically recognises that it is in a different location and if you have already mapped the rooms, it starts cleaning and you can control it as normal. When it is full (dust) or empty (water), it reports back. It also cleans several rooms without always wanting to return to the station. At the end of cleaning, you will receive a message "Cleaning finished" and "Station not found". You carry it back to the charging station and press dock, it recognises that it is back on the floor with the charging station and goes home. The app design is also specifically designed for this process.
So either use it as described above or, if money is no object, simply buy a second robot with a station... ;)