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Why would Koeman leave Southampton for Everton?!
I would go for Emery over De Boer. He's managed Sevilla and Valencia and did a good job in both roles. De Boer has only managed Ajax and whilst I believe he could do the job, it would be more of a risk.
I'd bring Phil Neville back to the club as a DoF - he's well connected, speaks Spanish and though people castigate him I believe he's got a pretty solid knowledge of football.
Emery and de Boer would be excellent choices, as would Koeman.
As for successful directors of football, how often do you see them move and replicate the success for which they have become known for?
At most clubs these men, they are pretty much all men, seem to have a long history in a number of roles at these clubs.
Someone like Giggs should be groomed to become a DoF at Man Utd.