A sequencer such as ableton live provides this functionality along with additional looping facilities.  You can switch from a multi-track recorder view such as described above to a loop-based view.  Here you can record segments as loops.  These loops can be varying length and you can record just about any number of loops an any of the tracks.  You might for example, devote some tracks to coming up with drum loops of varying lengths.  You can then play back these loops while recording a bass part into a loop of another track, and then another bass part into another loop on the bass track.  You can then go through this process of recording many of your parts into loops on various parts (e.g. various synth parts, rhythm guitar verse, rhythm guitar chorus, …).

Once you have your loops recorded, you can then do a live mix-down from your loop view to your multi-track studio view.  Here you are recording a live triggering and stopping of your recorded loops on different tracks that is then crating complete tracks in the multi track view.  You can then go on to switch to the multi-track view and edit your tracks in a similar way you would to a more traditional multi-track recording studio.

What I like about this sort of studio is that you can record a segment and start looping this segment on the fly without having to stop and cut an paste the segment with a predetermined structure in the multi track view.  This ability to loop on the fly can create a song writing process that can become more almost improvisational, without technology requiring you to stop and edit, that may really slow down the creative process.

Like it’s name, Ableton “live” can create a sort of live song writing and recording process, combining the best of multi-track recording and a spontaneous improvisation approach to playing music.