I've been working on this very thing with the last few tunes I have done.
On my soundclick site (links on my website) the song Missing Person (2012) has a total of 10 vocal tracks in it. The 2 leads are unison... in several places they (2 different singers) are singing together. They also sing solo in the track.
When they are solo, I have them panned 10% to a consistent side.... when they sing together, the panning goes to 35% or so to give them distance.
The 8 tracks of BGV are mixed much lower and panning is a bit more one sided, but there is balance. The 10 vocal tracks soloed as a group, present a fairly wide stereo image.
Now: I have also used 3 tracks as you describe. I generally use this to "thicken" the main solo vocal in a track. The song is not a "group sing" but is intended to be a solo preformance. I do choose one.... the better one IMHO to be down the center of the mix. It is set to the center of the stereo field and the level is up where the singer should be in the mix.
The other 2 tracks are panned R/L by at least 30% up to about 60% but generally no more. The panned tracks must be as close to perfect as possible to the lead. Timing, pitch, and all aspects of the performance of these tracks is critical. Especially the ending of words with s's in them.
I normally will send these tracks to a bus with a slight verb.... panned according to taste....and with levels set low. I want the levels so low that when I solo all the vocals I can barely hear the BGV tracks. Once the instrument mix is put into the picture..... that tends to mask the BGV a bit but they are still there, at the same level and the result is a thickening or fattening of the solo vocal track. I used this method on Ode To Wolf on the lead..... there are also harmony vocals in places where I kept the levels low to add the harmony without being too obvious with the singers...
I use envelopes a lot. Volume and panning. For example.... on Missing person... 2 singers in 2 different studios recording the unison vocal track...... no way will that come out picture perfect. And it didn't. In one place, my vocal sang a word and stopped..... Robby sang that same word and held it slightly longer. (the second time in the song ... "touch herrrrrr" right before the chorus) That is in a part of the song where we sang it together in unison..... the solution was to use the envelope to pull the level down on Robby's word so it ended with mine. The result sounds good. Same thing on the "s" sounds at the ends of words.... I use envelopes to make the ones not in sync disappear. One track ending properly will give completeness to that sound.... 3 ending slightly off from each other sounds sloppy.
There are no hard and fast rules. I have developed this method through trial and error and I know as time goes on these methods I currently use will evolve as I learn more about mixing.
Experiment and see what works for you.