In my company and as I suspect many others the Captain is cross qualified for both seats, on every OPC/LPC I will have a right seat competency check.
It provides for some flexibility in crewing an aircraft at times when no FO is available due sickness etc.
When operating right seat we are non handling except in an emergency and in my experience flying with other Captains has never created any problems. I would like to think that ones professionalism is employed in these circumstances.
As for two Captains in corporate flying, because of the sort of client you are carrying on many occasions and because the sort of people hiring corporate jets can afford it, two Captains are perceived to have twice the experience.