It only lets me go to 1st and 3rd. The people talk to me about Burnet's history and Battle Boxes, and the lady on the 1st floor just says "Youre going to the dimensional research lab right? its the only thing there after all." or something like that.
Currently, no, there is not. It's unknown if that floor even has any significance. Wouldn't be the first time a building in a Pokemon game had inaccessible floors.