A duplex with a basement apartment is just that: a duplex with a basement apartment. Most often there are two legitimate units with a legal non-conforming basement. This is not a triplex. If you have three self-contained units and you would like to change the legal status of your building, you have to go to your local municipal offices to find out more about how they zone and categorize multiple family dwellings. If you have a basement apartment that is “not legal” you must ensure that it meets all fire and safety standards. The fire marshal is not likely to force you to remove an apartment but you may be fined if you are in violation of your local fire code. If you are unsure about the legal status of your income property or would like to have it changed, consult with your attorney.