Possibly you could use FileSelectFile to manually select the files, then use FileRead and FileAppend.
Example:
Code:
FileSelectFile, firstFile,, C:\temp\, Choose the First File, Documents (*.txt)
FileSelectFile, secondFile,, C:\temp\, Choose the Second File, Documents (*.txt)
FileSelectFile, thirdFile,, C:\temp\, Choose the Third File, Documents (*.txt)
FileSelectFile, fourthFile,, C:\temp\, Choose the Fourth File, Documents (*.txt)
FileRead, firstFileContents, %firstFile%
FileRead, secondFileContents, %secondFile%
FileRead, thirdFileContents, %thirdFile%
FileRead, fourthFileContents, %fourthFile%
FileAppend, %firstFileContents%, newfile.txt
FileAppend, %secondFileContents%, newfile.txt
FileAppend, %thirdFileContents%, newfile.txt
FileAppend, %fourthFileContents%, newfile.txt