A mezzanine is, by definition, a floor offset a non-integral number of storeys from the floors around it; a floor existing at a fractional floor number, in other words. A mezzanine "between the first and second floor" (in american parlance) would have a floor offset of 0.5 (or possibly ranging from 0.3 to 0.7, since mezzanines usually involve complex arrangements of stairs and landings.)