This works perfectly but it would be nice if it were written more elegantly.

What it does is open spreadsheet files with month and year as part of the file name. It then copies a specific worksheet from each and pastes it back into a specific page of the spreadsheet that contains the macro. I'm thinking it would be easy to loop but I didn't know how to change my variable names with a loop:

Sub OpenDatedXLS()
'Open Workbooks with Date in Name of File.  Add or subtract months
Dim wb, wb1, wb2, wb3, fPath, fName As String
Dim MO1, MO2, MO3, MO4 As Date

fPath = ActiveWorkbook.Path & "\"
fName = ActiveWorkbook.Name

MO1 = Date
MO2 = DateAdd("m", -1, MO1)
MO3 = DateAdd("m", -2, MO1)
MO4 = DateAdd("m", -3, MO1)

sh1 = "SEA" & Format(MO1, "MMYY")
sh2 = "SEA" & Format(MO2, "MMYY")
sh3 = "SEA" & Format(MO3, "MMYY")
sh4 = "SEA" & Format(MO4, "MMYY")

wb1 = "PerDiemRatesForeignAreas_" & Format(MO1, "MMMMYYYY") & "Pd.xls"
wb2 = "PerDiemRatesForeignAreas_" & Format(MO2, "MMMMYYYY") & "Pd.xls"
wb3 = "PerDiemRatesForeignAreas_" & Format(MO3, "MMMMYYYY") & "Pd.xls"
wb4 = "PerDiemRatesForeignAreas_" & Format(MO4, "MMMMYYYY") & "Pd.xls"

Workbooks.Open fPath & wb1
    copysheetname = ActiveWorkbook.Name
    Worksheets(sh1).UsedRange.Copy
    Workbooks(fName).Activate
    pasterow = Workbooks(fName).Worksheets("Per Diem Rates").UsedRange.Rows.Count + 1
    Workbooks(fName).Worksheets("Per Diem Rates").Range("A" & pasterow).Select
    ActiveSheet.Paste
    Application.DisplayAlerts = False
    Workbooks(copysheetname).Close
    Application.DisplayAlerts = True
    
Workbooks.Open fPath & wb2
    copysheetname = ActiveWorkbook.Name
    Worksheets(sh2).UsedRange.Copy
    Workbooks(fName).Activate
    pasterow = Workbooks(fName).Worksheets("Per Diem Rates").UsedRange.Rows.Count + 1
    Workbooks(fName).Worksheets("Per Diem Rates").Range("A" & pasterow).Select
    ActiveSheet.Paste
    Application.DisplayAlerts = False
    Workbooks(copysheetname).Close
    Application.DisplayAlerts = True

Workbooks.Open fPath & wb3
    copysheetname = ActiveWorkbook.Name
    Worksheets(sh3).UsedRange.Copy
    Workbooks(fName).Activate
    pasterow = Workbooks(fName).Worksheets("Per Diem Rates").UsedRange.Rows.Count + 1
    Workbooks(fName).Worksheets("Per Diem Rates").Range("A" & pasterow).Select
    ActiveSheet.Paste
    Application.DisplayAlerts = False
    Workbooks(copysheetname).Close
    Application.DisplayAlerts = True

Workbooks.Open fPath & wb4
    copysheetname = ActiveWorkbook.Name
    Worksheets(sh4).UsedRange.Copy
    Workbooks(fName).Activate
    pasterow = Workbooks(fName).Worksheets("Per Diem Rates").UsedRange.Rows.Count + 1
    Workbooks(fName).Worksheets("Per Diem Rates").Range("A" & pasterow).Select
    ActiveSheet.Paste
    Application.DisplayAlerts = False
    Workbooks(copysheetname).Close
    Application.DisplayAlerts = True

End Sub