I don't think you can do this in Logic. You can only have one audio file at a time playing through a channel strip. A single audio channel strip can't handle multiple files simultaneously.
You can cycle record and build up an arrangement consisting of the multiple passes. But you'll need to assign each of them to unique channel strips after the recording. You won't be able to keep hearing the previous takes as you add new ones all in real time as you are cycle recording.
I may be wrong; but I can't think of a way to do what he wants in Logic. It sound like he wants "drum machine style" loop recording - where you keep adding parts on each pass - but with audio.
I have a question in a similar vein, (so I chose to keep it in this thread)...what about looping midi/soft instruments and recording an audio file in linear (ie non-looped or cycled) fashion? Obviously, I can create region alias' to represent cycled material, but then I'd have to pick a length, when maybe i'd like to just hear the looped midi, but record free-form without worrying how many bars I have left. Is there a way for Logic to do this?