Certainly is possible. Have a look at this video http://www.youtube.com/watch?v=nw80Wr0EuoI
and then this one for a little more detail http://www.youtube.com/watch?v=npJyywE9ju8
Lots more interesting stuff here too: viewtopic.php?f=4&t=10807
Hope this answers your question.
They all have their limited use, but none of them are really dealing with the OP's request. Nick, this is how to do it:
Record 4 full takes on 4 separate tracks.
Starting at the front of the song, listen to each small phrase on all 4 tracks one by one. Choose the 'best' one, split it at front and back of the phrase. Listen to the split clip to
make sure you have exactly the right part of the phrase, adjusting the front and back of the clip carefully until you have it. Including a bit of vocal before the beginning and/or a bit after the end is not good enough. You want the exact phrase. Zooming in close will help with this.
Highlight the clip, then move it up to an empty audio track using the up arrow. (This will ensure that you don't accidently move the clip sideways out of time when moving it). Repeat this procedure with each phrase until you have your composite vocal. Make sure all edits are slightly overlapping each other. Zoom in to perform each overlap (called a 'crossfade') because you want as little overlap as possible.
Now solo the comped vocal and monitor back, checking for errors, bad edits, etc.
Don't ever use the 'merge' function. It's unstable, buggy, call it what you will, but it's unreliable.