Well, if the question is whether that's all the Commanders in the film or not, that remains to be seen. I don't think Thire stood out from any of the others, did he? But anyway, if the question is whether or not there are more Commanders in the Republic military I think it's pretty well inevitable there would be.
Every group of Clones is going to have a field Commander I'm guessing... That's also my only logical conclusion on what the actual title "Commander" means. It's a rank unique to Star Wars as Commanders aren't usually marching in with the men in Earth combat terms, not like Cody did anyway, so I've been grappling with the title "Commander" being used in the Clone military for a long time now (Since AOTC).
But underneath every Commander I figure there has to be Captain's, Lieutenant's, and then the groupings of Non-Coms and Troopers. I figure there's not much structure for troopers other than they have a Sergeant of perhaps varying degrees, but the build up to the rank of Sergeant (IMO) is non-existant and till you gain that higher level below officers you are just a "Trooper". It simplifies things at least.
Beyond that you have sergeants... Do they look different? Perhaps in some units, but not in others. With the color coding done away with between the early war and the late war, I figure some means of identification of rank was conceived otherwise. So Sergeants of all levels (I figure the "dots" on the chest of the early War Clones represented varying levels of rank for that rank level. It's the only thing I can think of anyway) would, in my mind, look like other Clone Troopers... Maybe they are the troop designated to carry the support weapon (Blaster Carbine) or whatnot?
From there the Clones have Lieutenants of varying degrees, Captains... Then that odd rank of "Commander". Somehow above a Captain, though the actual rank of "Commander" in Naval terms is underneath a Captain so that's confusing, and I don't believe there is a rank of Commander within the Army or Marines... Only Navy, however there is no Sergeant within the Navy if I'm thinking right (actually a whole other ranking structure really) so again there's a confusing notion.
The rank of Colonel and the rank of Major appear to be completely glossed over in at least the Clone military structure.
Like Sergeants though I figure the dots of the early war Clones represented various levels of rank within the Lieutenants, then the Captains (which in military terms is goofy because there is only one rank of Captain for the Army, Navy, etc., but whatever), etc.
Commander then still remains an enigma. It's below the rank of Captain within the Navy but in the Clone world a "Commander" outranks a Captain. This again leads me to believe the full title is "Field Commander", and this ranking trooper on the field is a liason between the Jedi General (or potential sentient officers commanding a battle situation? I do believe that the Republic HAD a standing military and Officers who would comprise a military body outside the Clones. In the CW cartoon we see a ground crewman for instance around the Clone fighters, and also I've read that people like Jan Dodonna were up and coming officers in the war... Also cut lines from ANH had Red Leader saying he fought with Luke's father, etc., so I'm sure there were more than Clones running the show and don't believe them to be the guys running Destroyers and things). The Field Commander or "Commander" is the most adept, respected, and dangerous soldier on the field short of possibly special ops troopers such as Commandoes and ARCs, and he's there for leadership and coordination where the Jedi cannot always be there to be the leaders on the field.
Some lower ranks within a Clone Legion (I'm guessing Legions are the largest single military grouping in the Star Wars Galaxy) maybe are allowed to adjust their armor by the whims of their COmmander or Jedi General? Perhaps all Clones are allowed to modify their gear even, further setting them apart from others? Lots of room for debate and thought there.
Also, a point of note about Appo (always wanna call him Alpo) and Fox... Fox cannot possibly be second in command in my mind. Sergeants don't run the show unless everyone's dead, so if Appo is a legion Commander ("Field Commander", whatever), I believe Fox must be at the least a Captain (by the generally accepted EU guide to Clone ranks). Sergeants just don't lead large groups like that unless they work their way to a higher rank due to casualties within the ranks, field promotion for exemplary work, etc...
I could see Fox as an aide, or liason that Appo uses to communicate with his various other lower ranking officers. It's likely any Commander in the field would have men of some substance grouped around him to send personal messages, to defend him if need be, etc...
These are just some thoughts on Clones and "Commanders"/Officers throughout the Prequals. They really did a piss poor job in covering this stuff in EU materials and the films. The films never really get into the lower ranks though so all these names/ranks are basically EU aside from Cody who Kenobi talks to directly by his name and using the "Commander" term with him. Again one could argue though that "Commander" is a generic title for any ranking Officer and that it's not a literal term.
The term "Commander" is used liberally throughout the classic trilogy like that. Jerjerrod is listed as Moff Jerjerrod in the credits I believe but called Commander by Palpatine because he's the Death Star's ranking officer. I personally view his title of Moff as his rank though as EU says, but he's still a "Commander" of men. That's all just food for thought.
A lot to be said about Clone ranks. I've never much liked its layout in EU though. The people who created the ranking structure never accounted for the dot patterns on the left chest and stuff, they just slapped "Sergeant = Green, Lieutenant = Blue, Captain = Red, and Commander = Yellow" to them, which is just lazy on someone's part.
Same happened with the Pauldrons for the (I believe to be mythical) "Sand"Trooper. For my money, the pauldrons and modular packs are standard gear for Imperial Stormtroopers in ANY field condition aside from extreme cold/'mountainous. To me the cold/mountain gear is the "Snow"Trooper gear and I don't buy there actually being "Snow"Troopers that are ready at a moment's notice to drop onto icy planets... just in case.
It's easier in my mind to assume that Stormtroopers have clothes for cold weather assaults, and that the Standard Trooper armor is used for other climates and the pack is modular to be adapted with the appropriate gear for the appropriate world. THe Pauldron then is a FAST means of identifying ranking individuals on the field. The Orange Pauldron isn't indicative of any specific rank, and could indicate anything from a Lieutenant up to a General in armor even. The other colors are a little more believable though for what they were listed, and there's lotsa EU designs I dig too.
Anyway this is rambling a bit about how ****** military organization has gotten since the classic trilogy was made. EU has taken some great steps to coordinate it, but with the prequals they've made a ****** effort at best. It doesn't help when Lucas makes umpteen unique Clone designs for his final prequal film as a marketing technique... As cool as they are and all.