Использовать массив.
Sub Merge2MultiSheets()
Dim xRg As Range
Dim xSelItem As Variant
Dim xFileDlg As FileDialog
Dim xFileName, xSheetName, xRgStr As String
Dim xBook, xWorkBook As Workbook
Dim xSheet As Worksheet
Dim vDB As Variant '<~~ new Variable for array
Dim Target As Range 'new Variable
On Error Resume Next
Application.DisplayAlerts = False
Application.EnableEvents = False
Application.ScreenUpdating = False
xSheetName = "Sheet1"
xRgStr = "A1:D4"
Set xFileDlg = Application.FileDialog(msoFileDialogFolderPicker)
With xFileDlg
If .Show = -1 Then
xSelItem = .SelectedItems.Item(1)
Set xWorkBook = ThisWorkbook
Set xSheet = xWorkBook.Sheets("New Sheet")
If xSheet Is Nothing Then
xWorkBook.Sheets.Add(after:=xWorkBook.Worksheets(xWorkBook.Worksheets.Count)).Name = "New Sheet"
Set xSheet = xWorkBook.Sheets("New Sheet")
End If
xFileName = Dir(xSelItem & "\*.xlsx", vbNormal)
If xFileName = "" Then Exit Sub
Do Until xFileName = ""
Set xBook = Workbooks.Open(xSelItem & "\" & xFileName)
Set xRg = xBook.Worksheets(xSheetName).Range(xRgStr)
vDB = xRg '<~~ Put the contents of a range into an array
'xRg.Copy xSheet.Range("A65536").End(xlUp).Offset(1, 0)
Set Target = xSheet.Range("A65536").End(xlUp).Offset(1, 0)
Target.Resize(UBound(vDB, 1), UBound(vDB, 2)) = vDB '<~~ Get the value of an array.
xFileName = Dir()
xBook.Close
Loop
End If
End With
Application.DisplayAlerts = True
Application.EnableEvents = True
Application.ScreenUpdating = True
End Sub