This one will append the new data to the existing

Option Explicit
Option Base 1

Sub CollectWorkbooks()

Dim varFiles As Variant
varFiles = Application.GetOpenFilename("Excel-files,*.xls; *.xlsx; *.xlsm", _
    1, "Select Workbooks to Collect", , True)
'exiting if no files were selected
On Error Resume Next
If UBound(varFiles) = 0 Then
End If
If Err.Number = 13 Then Exit Sub
On Error GoTo 0
Application.ScreenUpdating = False
Application.DisplayAlerts = False
Dim n As Long, r As Long
Dim f As Integer, s As Integer

Dim wbSource As Workbook, wbMaster As Workbook
Dim shSource As Worksheet, shDest As Worksheet
Set wbMaster = ThisWorkbook


'opening each file and importing the data
For f = 1 To UBound(varFiles)
    Set wbSource = Workbooks.Open(varFiles(f), ReadOnly:=True)
    For Each shSource In wbSource.Worksheets
        'getting the same sheet in the master file if it exists
        Set shDest = Nothing
        On Error Resume Next
        Set shDest = wbMaster.Worksheets(shSource.Name)
        r = shDest.Cells.SpecialCells(xlCellTypeLastCell).Row
        On Error GoTo 0
        'if the sheet doesnt exist then create it
        If shDest Is Nothing Then
            Err.Clear
            Set shDest = wbMaster.Worksheets.Add(after:=wbMaster.Worksheets(wbMaster.Worksheets.Count))
            shDest.Name = shSource.Name
            r = 1
        End If
        'adding the records
        r = r + 1
        n = shSource.Cells.SpecialCells(xlCellTypeLastCell).Row
        s = shSource.Cells.SpecialCells(xlCellTypeLastCell).Column
        shSource.Range(shSource.Cells(2, 1).Address & ":" & shSource.Cells(n, s).Address).Copy _
        Destination:=shDest.Range(shDest.Cells(r, 1).Address & ":" & shDest.Cells(r + n, s).Address)
        
    Next
    wbSource.Close

Next
Application.ScreenUpdating = True
Application.DisplayAlerts = True
End Sub