I use doubling and harmony a lot.
My song Missing Person (2012)
http://www.soundclick.com/bands/page_songInfo.cfm?bandID=443134&songID=11962059 has 10 vocal tracks. 2 singers with 1 main and 2 doubles and 2 harmonies each.
Footsteps has 5 vocal tracks
http://soundclick.com/share.cfm?id=12048139 On any given project my average solo project has 5 vocal tracks in the end mix. One is lead. the second and third tracks are also lead vocals that have been recorded live, never cloned. I keep the main vocal centered and about -6db but that level really depends on the way it sets in the mix. No FX in the track. Set up a vocal bus for reverb and EQ with all 3 leads going there. Pitch correct the lead vocal track and perhaps the doubles. The key to avoiding the flangy, phasey sound is to pan the 2 doubles wide..... 80% or more and keep the levels on them somewhere around -24db. This level will be set by trial and error but -24 is the starting point. My aim is to let these tracks add a slightly fuller sound without being obvious. In other words, I can't really hear them in the main mix, but if I solo the vocal bus I can hear the doubles.
On the fourth and fifth tracks,,,,,, harmony tracks, these too are recorded independently. I pan them 50% to 80% in most projects and use -16db as the starting point. I want the harmonies to "fill in" the vocal in the chorus and other places where I have them. Generally, I like a subtle harmony presence. You do have the choice to bring them up and create a "Statler Brothers" kind of harmony where all the harmony vocals have equal billing in the sound stage. I do not generally like to use that method of harmony but will do it as the song demands. I also will very often put the harmony tracks in their own bus and add a slightly heavier reverb to them. Nothing crazy, just something that moves them "back" a bit.
This is how I record vocals and harmonies. If you clone the lead, you will have exact duplicates of the tracks and more issues with comb filtering and for that reason I always record independent tracks. Even so, I have to be careful to avoid the comb filtering that is possible with three very similar tracks. Keeping the levels low on the doubles will help immensely in that area. It still gives you the fatter doubling but at more of a subconscious level and it leaves the main vocal sounding cleaner. To see if you can hear the difference, simply use the GROUP function to group both of the doubled/panned vocal tracks and then as the song is playing in the parts where there is not harmony vocals, use the mute to mute and unmute the 2 doubles during playback.
Anyway.... that's how I do it. hope this helped you.