Insert rows instead of copying rows

I am looking for help with a macro who is coping a "named range" from a sheet that contains a large list of named ranges.

The active sheet has 20 or more named ranges. This list can grow and shrink.

The macro below is everything what I need, but, the macro is not moving data but overwriting other data.

When the named range is copied it will need to move and insert the data in the active sheet, not overwriting.

For testing purposes I created 3 name ranges: "ABC", "DEF" and "GHI".
(attachment is anonymised)

Is that possible?

Private Sub CommandButton1_Click()

    If ListBox1.ListIndex = -1 Then Exit Sub
    Dim cell As Variant
    On Error Resume Next
    Set cell = Application.InputBox("Choose a destination cell to paste ", "Input Destination", Type:=8)
    If cell Is Nothing Then Exit Sub
    Range(ListBox1.List(ListBox1.ListIndex)).Copy cell
  
End Sub

Private Sub UserForm_Activate()
    
    Dim i As Long, refer As Variant, ss As Variant
    For i = 1 To ActiveWorkbook.Names.count
        refer = ActiveWorkbook.Names(i).Name
        If Not IsError(refer) Then
            If Left(refer, 2) <> "_x" Then
                ss = ActiveWorkbook.Names(i).RefersTo
                If InStr(1, ss, "ProjectSchedule", vbTextCompare) > 0 Then
                    ListBox1.AddItem refer
                End If
            End If
        End If
    Next

End Sub

Thank you, Henk.