can you loop record a real instrument track not as takes?

I would like to record a real instrument (external microphone) in a loop, however is it possible to not do this as takes but instead add to one loop on every rotation? I am interested in doing this so that there is a one loop delay between recording and playback and every previous looped recording is re recorded with the next so as to combine the multiple recordings in one loop.

Alternatively is this possible in Mainstage if not possible in Logic?

Thanks