Copying data from other workbooks and pasting into master workbook

This is my guess work on what you are trying to do.
You should have master book with sheet1 as a destination sheet. Sheet1 has also a header.

Sub Collect_Data()

  Dim DstWks1 As Worksheet, DstWks2 As Worksheet, LastRow As Long, NR As Long, SrcWkb As Workbook, StartRow As Long
  Dim wkbname As Variant
  Dim xlsFiles As Variant
  Application.ScreenUpdating = 0

   'Set references to destination workbook worksheet objects
    Set DstWks1 = ThisWorkbook.Worksheets("Sheet1")
    Set DstWks2 = ThisWorkbook.Worksheets("Sheet2")

   'Starting row on source worksheet
    StartRow = 1
    
   'Get the workbooks to open GetOpenFilename
   
    xlsFiles = Application.GetOpenFilename(FileFilter:="Excel files (*.xls*),*.xls*", MultiSelect:=True) 'Excel files (*.xls),
    Application.AskToUpdateLinks = False
      If VarType(xlsFiles) = vbBoolean Then Exit Sub
      
     'Loop through each workbook and copy the data to this workbook
      For Each wkbname In xlsFiles
        Set SrcWkb = Workbooks.Open(fileName:=wkbname, ReadOnly:=True)
        With SrcWkb.Worksheets(2)
            LastRow = .Cells(.Rows.Count, "D").End(xlUp).Row
            .Range("A2:D" & LastRow).Copy
            NR = DstWks1.Cells.Find("*", , , , xlByRows, xlPrevious).Row + 1
            DstWks1.Range("A" & NR).PasteSpecial xlValues
        End With
         Application.ScreenUpdating = True
        SrcWkb.Close SaveChanges:=False
        ''SrcWkb.Close''
      Next wkbname
      
End Sub