Okay this is better than the solution I came up with, but you seem to be way more of a VBA expert than me, but would his have worked just as well, or is there a reason your "With" solution is superior?
Sub copier()
'Creates Row Offset Variable'
Dim y As Integer
y = 0
Dim x As Integer
Application.ScreenUpdating = False
NumRows = Range("A1", Range("A1").End(xlDown)).Rows.Count 'Number of rows in sheet'
Range("A1").Select
' Establish "For" loop to loop "numrows" number of times.
For x = 1 To NumRows
Dim z As Long
'Number of times to copy row'
For z = 1 To 10
Rows(1 + y).Insert
Rows(2 + y).Copy _
Destination:=Rows(1 + y)
Next z
y = y + 11
Next
End Sub