Can you make a new gamecentre account, but keep progress on games?

My two sons both play games using gamecentre. Their Clash of Clans villages are different, even though they are playing using the same gamecentre account. My oldest son has bought a new phone and wants to get his clash of clans on the new phone, but when he logs in to gamecentre using his profile, he gets his brother's village and not his, for some reason.

I think the solution is probably to create a separate gamecentre profile for each of them, but the one with the new profile will need to transfer all game progress, achievements, etc to the new profile if this is going to be an acceptable solution.

Does anyone know how we can tackle this thorny issue, before actual clash of brotherly clans breaks out in my house?

thanks