I think there are a few ranks that must fall outside the main hierarchical system.
Arbat, for example, was an Apex level intelligence officer or something. Where does that fit? Simply put, I think it doesn't, because it's simply a different profession than the main military.
Same with First Officer and Tactical Officer, which are supporting positions within a ship, and probably don't fit in amongst aristh and Warrior and so on. In cases like that, they may have a military rank in addition to their position within the ship. Perhaps the First Officer is also a Prince? I don't really know, mind you, I'm just guessing. This is just what would make sense to me.
Force-Commander may be the same sort of thing, though. He was directing the forces on a planet, which is fairly different from the standard Andalite tactics of war in space. It could be that such positions are just outside the system.
Good question, though. As you can probably tell, I've thought about this before.