I noticed that there is no need for copying. Apparently when adding an instance of a model to the database (even if the ID is set to one that already exists in the database), Entity Framework inserts a new row in the database and auto-increments it’s primary key. So this functionality is already built-in into EF. I didn’t know this, sorry.
Just for clarity’s sake here is an example:
using(var database = new MyDbContext()) {
MyModel myModel = database.FirstOrDefault(m => m.SomeProperty == someValue);
myModel.SomeOtherProperty = someOtherValue; //user changed a value
database.MyModels.Add(myModel); //even though the ID of myModel exists in the database, it gets added as a new row and the ID gets auto-incremented
database.SaveChanges();
}