I still think an Apple Script would be easiest, especially if you already know how many documents there are, where they are, and how you want to combine them (blank line between documents, line of characters between each one, nothing, etc.). Frankly I've yet to find anything that Automator can do that doesn't require AS, anyway. It gets one close to what is needed but lacks basic for/else steps that are needed for so many things.
Variables are available but I've never seen a way to use them in a Loop or much of anything else. Probably just me. Anyway, give AS a try, you can point a script to the collection of files you want to use, make it open and copy the text, and paste it into a default document. That basic action, of course, needs to be repeated for each original document until all have been read and concatenated to the end of the previous one. Then, save the new, large file.
Of course, if you have FileMaker, it is a fairly simple task to import each document as a new, single field text record and then create a final record as the sum of each text record.
One other alternative is to teach your cat how to do his...
