I think the best cooperation is in terms of emergency rescue, backup communications, and sharing scientific results.
Emergency rescues mean compatible docking systems to that if an opportunity arises technical problems don't stop the rescue. Of course actually catching something in space in time to pull off a rescue is nearly impossible, but just in case the orbits line up...
Emergency rescue also means that moon/mars missions should plan to land ~10km from each other - while the area of exploration is greatly limited it means in the worst case you can walk to the other for safety. It also means a party in the middle one day - moral is itself an emergency.
Backup communication means that radio frequencies are compatible. That way "our relay can't reach our rover" can turn to "but we can - let us control it".