Since both Captain America and Thor have their own corps, I searched and wondered why Iron Man didn't have one, I thought since he Captain America and Thor are Marvel's big three, why not give him his own corps. So based off the character similarities between the pre-existing corps, I am making my suggestion for the corps.
Captain America - Thor; The leader of course will be none other than Iron Man
Winter Soldier - Beta Ray Bill; Bringing in Warmachine to play the part of the loyal sidekick
USAgent - Thunderstrike; The anti-hero counterpart would be Guardsman
Commander A - Dargo Ktor; I know there is Iron Man 2020 who could be the future Iron Man, but I think it could be better if the future Iron Man was from the same time period as Commander A and Dargo Ktor, so I am suggesting Silver Centurion (which is also a name of one of Iron Man's armors)
American Dreamer is the only Captain America Corps member that doesn't have a Thor Corps counterpart, but that could be easily fixed by bringing in Thunderstrike from the MC2 timeline, of course I would change his name to Thunderstrike Jr. as he is the son of the other Thunderstrike, and Iron Man's MC2 counterpart would be Mainframe
I also wanted to add in my own addition to each team, Agent 66 - Lady Sif - Rescue (Pepper Potts) as the female counterparts/love interests.