Auto-increment a primary key in the LINQ to SQL DataContext “Insert” partial method

What I would like to do is the following. I have a single table, Products, containing a private key ProductID. Instead of having SQL Server auto-increment ProductID on inserts, I want to increment it in the DataContext partial method "InsertProduct":

Partial Public Class MyDataContext

    Private Sub InsertProduct(ByVal instance As Product)

        Dim id As Integer = Me.Products.Max(Function(p As Product) p.ProductID) + 1
        instance.ProductID = id

        Me.ExecuteDynamicInsert(instance)

    End Sub

End Class

However, this will only work when inserting the first Product instance. When attempting to insert a second instance, the id retrieved is the same as for the first,

Using context As New MyDataContext

    Dim product1 As New Product
    context.Products.InsertOnSubmit(product1)
    context.SubmitChanges() 'This works

    Dim product2 As New Product
    context.Products.InsertOnSubmit(product2)
    context.SubmitChanges() 'DuplicateKeyException

End Using

Am I missing something obvious here?