Please ignore last post - back on track again.
Stepping through the program using F8, Filename 1 pastes to A2-A31 then sheet 4 data is pasted into B2-B31, then sheet 6 is pasted into B32-B61. Filename 2 pastes to A32-A61 and the next sheet 4 overwrites the previous data.
Need Filename 1 A2-A61, sheet 4 cells to B2-B31, sheet 6 cells to B32-B61, then
Filename 2 A62-A121, sheet 4 cells to B62-B91, sheet 6 cells to B92-B121 etc., etc.
Cannot see how to increase the offset in column A with there being a knock on effect.
Can anyone see how this could be modified?

Current code:
Sub MergeAllWorkbooks()
    Dim MyPath As String, FilesInPath As String
    Dim MyFiles() As String
    Dim SourceRcount As Long, FNum As Long
    Dim mybook As Workbook, BaseWks As Worksheet
    Dim sourceRange As Range, destrange As Range
    Dim sourceRange1 As Range, destrange1 As Range
    Dim rnum As Long, CalcMode As Long

    ' Change this to the path\folder location of your files.
    MyPath = "C:\temp1"


    ' Add a slash at the end of the path if needed.
    If Right(MyPath, 1) <> "\" Then
        MyPath = MyPath & "\"
    End If

    ' If there are no Excel files in the folder, exit.
    FilesInPath = Dir(MyPath & "*.xl*")
    If FilesInPath = "" Then
        MsgBox "No files found"
        Exit Sub
    End If

    ' Fill the myFiles array with the list of Excel files
    ' in the search folder.
    FNum = 0
    Do While FilesInPath <> ""
        FNum = FNum + 1
        ReDim Preserve MyFiles(1 To FNum)
        MyFiles(FNum) = FilesInPath
        FilesInPath = Dir()
    Loop

    ' Set various application properties.
    With Application
        CalcMode = .Calculation
        .Calculation = xlCalculationManual
        .ScreenUpdating = False
        .EnableEvents = False
    End With

    ' Set worksheet for information to be merged to.
    Set BaseWks = Worksheets(1)
    rnum = 2

    ' Loop through all files in the myFiles array.
    If FNum > 0 Then
        For FNum = LBound(MyFiles) To UBound(MyFiles)
            Set mybook = Nothing
            On Error Resume Next
            Set mybook = Workbooks.Open(MyPath & MyFiles(FNum))
            On Error GoTo 0

            If Not mybook Is Nothing Then
                On Error Resume Next

                ' Change this range to fit your own needs.
                With mybook.Worksheets(6)
                    Set sourceRange = .Range("b5:b34")
                With mybook.Worksheets(4)
                    Set sourceRange1 = .Range("b5:b34")
                End With
                End With

                If Err.Number > 0 Then
                    Err.Clear
                    Set sourceRange = Nothing
                Else
                    ' If source range uses all columns then
                    ' skip this file.
                    If sourceRange.Columns.Count >= BaseWks.Columns.Count Then
                        Set sourceRange = Nothing
                    End If
                End If
                On Error GoTo 0

                If Not sourceRange Is Nothing Then

                    SourceRcount = sourceRange.Rows.Count

                    If rnum + SourceRcount >= BaseWks.Rows.Count Then
                        MsgBox "There are not enough rows in the target worksheet."
                        BaseWks.Columns.AutoFit
                        mybook.Close savechanges:=False
                        GoTo ExitTheSub
                    Else

                        ' Copy the file name in column A.
                        With sourceRange
                            BaseWks.Cells(rnum, "A"). _
                                    Resize(.Rows.Count).Value = MyFiles(FNum)
                        End With

                        ' Set the destination range.
                        Set destrange = BaseWks.Range("B" & rnum)
                        Set destrange1 = BaseWks.Range("B" & rnum + 30)
                        ' Copy the values from the source range
                        ' to the destination range. Overwrite is here
                        With sourceRange
                            Set destrange = destrange. _
                                            Resize(.Rows.Count, .Columns.Count)
                        destrange.Value = sourceRange.Value
                        End With
                        With sourceRange1
                            Set destrange1 = destrange1. _
                                            Resize(.Rows.Count, .Columns.Count)
                        destrange1.Value = sourceRange1.Value
                        End With
                        rnum = rnum + SourceRcount
                    End If
                End If
                mybook.Close savechanges:=False
            End If

        Next FNum
        BaseWks.Columns.AutoFit
    End If

ExitTheSub:
    ' Restore the application properties.
    With Application
        .ScreenUpdating = True
        .EnableEvents = True
    End With
End Sub