Can you take part in caravan security with a player who is affiliated with a different Grand Company?

Nope, you won’t be able to join in the operation with a member of a different Grand Company. Also, you will only be able to take part in caravan security from the aetheryte associated with your Grand Company’s city-state. For example, only members of Ul'dah's Immortal Flames can join the caravan security operation in Camp Horizon.
Guess no ones doing these..