No. If an apartment has a loft or mezzanine where part of the apartment has high ceilings and the other part has 2 levels, you do not count the loft or mezzanine as a separate story.
Only count full stories where there are hallways and elevators.
However, you should include the square foot of the mezzanines/lofts in your property’s Gross Floor Area (GFA).
Portfolio Manager does not explicitly ask for number of stories, but you do have to categorize your buildings as high rise/mid rise/low rise. So, for example if you have an 8 story building and 4 floors are taller with 'loft' space, you should still consider that 8 stories (which is mid-rise).