Update Master spreadsheet from multiple templates sheets

Would the templates be found in a specific folder, or would they arrive as email attachments?

Create another sheet in the Master workbook called Templates. A1 = "Folder", B1 = "Template" for headings. Enter your folder and heading names beneath. If all the templates will be in the same folder, then you can just enter it into B2 and adjust the code to use B2 for all folders.

Add the code below to the Templates sheet, and if you want, add a "Get Template Data" button to run the code, or you can just assign it to a shortcut key.

Option Explicit
Dim Folder As String, Template As String
Dim mrow As Long, trow As Long, tnamerow As Long, mcol As Long

Sub GetTemplateData()
    Application.ScreenUpdating = False
    Sheets("Templates").Select

    With Sheets("Sheet1")
        mrow = .Range("A" & Rows.Count).End(xlUp).Row + 1
        mcol = .Range("A1").End(xlToRight).Column
        tnamerow = 2
        Do Until Cells(tnamerow, 2).Value = ""
            Folder = Cells(tnamerow, 1).Value
            Template = Cells(tnamerow, 2).Value
            If Right(Folder, 1) <> "\" Then
                Folder = Folder & "\"
            End If

            Application.StatusBar = "Opening " & Template
            Workbooks.Open Folder & Template
            trow = Range("A" & Rows.Count).End(xlUp).Row
            Range(Cells(2, 1), Cells(trow, mcol)).Copy Destination:=.Cells(mrow, 1)
            ActiveWorkbook.Close (False)

            mrow = .Range("A" & Rows.Count).End(xlUp).Row + 1
            tnamerow = tnamerow + 1
        Loop

        Application.StatusBar = False
    End With
End Sub

Here is a formula based solution that would require that all workbooks retain theirs names and be open at the same time in order for this to work.
I inserted a column at Column A of all the workbooks. In the sub workbooks there is a formula that numbers the rows that have data. This is the formula entered into A2 of each sub workbook:

Formula:

=IF(B2<>"",MAX($A$1:A1)+1,"")

In A1 of each sub workbook except the first this formula to retrieve the max value from column A of the previous workbook is used using the name of the previous workbook in the series :

Formula:

=MAX('[Example Template 1.xlsx]Sheet1'!A:A)

All of the max values in the workbooks is brought forward to the Master workbook with this formula. The names of the workbooks for this example are in BN3:BN5 and this formula is entered in BO3 and filled down:

Formula:

=MAX(INDIRECT("'["&BN3&".xlsx]Sheet1'!A:A"))

The above values are then used in column A of the Master workbook to determine how many rows to assign to each workbook. This formula is entered into A2 and filled down:

Formula:

=IF(ROWS($1:1)>MAX(BO:BO),"",INDEX(BN:BN,MATCH((ROWS($A$1:A1)-1),BO:BO)+1))

Then to retrieve the data from each workbook the following VLOOKUP formula is entered into B2 and filled across and down:

Formula:

=IFERROR(VLOOKUP((ROWS($A$2:A2)-1)*1+1,INDIRECT("'["&$A2&".xlsx]Sheet1'!A2:BB400"),COLUMNS($A$1:B1),0),"")

Here are your workbooks setup so that you can try out the setup.

Trouble uploading workbooks. I'm trying again.