I'm not sure...does AHJ mean the Authority Having Jurisdiction? From what I've heard they shouldn't have a problem with it. But I was hoping to better verse myself on what the NEC says. And so far all I've seen in the NEC is a reference to Type III, IV, V Buildings in the NFPA. When I read Article of 220 in the NFPA I see a lot about Fire Ratings, and not so much about the amount of stories or levels, or the concrete. Does the NFPA delineate on Fire Ratings of Materials?
I guess I have to ask this question....Do you own a copy of the National Electrical Code? The reason I ask is due to the references you are giving and wondering why you would be in Article 220 if you are asking about the use of Nonmetallic-Sheathed Cable for use in a commercial building.
The first answer lies in Section 334.10(3)....next in order to understand what Type III, IV and V construction is the best reference would be to review the International Building Code (IBC) as that governs the construction (for the most part) of the buildings. However, you can also look at Informative Annex E in the NEC for classic descriptions as well.
Reading Section 334.10(3) is rather simple, comply with the approach and understand a few things. Is the building being built out of entirely concrete because it is required to be or because it is elected to be by the designer due to height limitations and so on. Once that is established then you can move on, some buildings are built to Type I and II Construction but could have been Type III, IV or V but elected to go for Type I or II.....if that was the case then nonmetallic -sheathed cable is fine.....just follow the rules in Article 334.
If the building is required to be of the Type I or II Construction then that does not rule out the use of Type NM Cable(regardless of height...but beware of installing above suspended ceilings), you just have to follow the rules demanded in Section 334.10(5) and install a raceway that is permitted in that type of construction first...just keep in mind of securing and supporting rules and other limitations found in Article 334...most notably those in Section 334.12.
Anyway...hope I did not confuse you...and I am sure my words will be picked apart looking for accidental misspoken examples...but it's a start for you.
P.S. I would not worry about this building being a Type III, IV or V Construction....regardless of knowing those are associated with wood framing....the number of stories alone tell you it can't be those types. I would recommend using Type MC Cable if you are looking for flexibility and easy of installation.