It's the most atrocious thing ever when you hear it solo'd
Basically I used 3 tracks:
Main track: Just the vocals, processed like any other vocal track
Shifted track: I took the main track, split notes and shifted them with Reaper's built-in function (without even correcting formants) until they made a 4th/5th interval, to blend with the backing vocals (3rd), making a fuller-sounding 3 note chord. Then I pitch shifted everything with Reapitch one octave up and one octave down (+/-9 semitones formant correction, standard algorythm, -9dB blended with original)
Backing track: Pitch shifted the provided backing track just like the shifted track, but without altering the notes.
Finally used waves Doubler2Stereo to pan to the sides both backing tracks, leaving the main track in dead center.
Here's the rendered tracks separately for the chorus section:
https://dl.dropboxusercontent.com/u/425433/Mixes/vocals atr.zip
That's something I use a lot in other productions, pitch shift and double, to create the illusion of separation and choir-like chrouses.
EDIT: Levels are wrong as you might probably notice when you open the files, they should be much lower, but I forgot the master buss on when rendering, so every track was individually maximized...