Can anyone ID this shrub?

JackTerp

5 year old buck +
A fella stopped by the house today and asked if he could get some cuttings off this shrub. He said it was a dogwood that the deer loved. It is evergreen and I do not think it's a dogwood. Any idesas?

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Very low confidence, but could it be bayberry? Evergreen, waxy purple berries. Boil some and if you get a coating of wax on top of the water, it could be bayberry.
 
Might be a better picture.

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Looks like Japanese privet to me... Jack, you appear to have invasives as bad as I do!
 
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