Since you asked how, I can tell you what I would try from a blind start (below).
We asked "what you had to start with" meaning the sound of what you are starting with; the tracks. Some here may be able to tell you exact settings on given effects IF they had a sample of what you are starting with. Maybe even a TGS file all set up and ready to go.

One approach:
Picture a stage with the lead singer in center.

Picture where the other vocalists are and pan your backups to suit.
Put a reverb on them and try panning the reverb to either be coming from the opposite side, or from behind them. It most likely should be different than the main reverb on the vocals and mix. Separate reverb on a buss for the backups or applied to each track.
Many times a 'Plate' type reverb can be used for this type of backing since it is pretty well buried. Play with the predelay on the reverb; it is as important as the tail and the volume for this effect.

Eq the bottom end out (another reason some may not hear them). Whole different sound intentionally. Think 'above the main vox' in frequency, but not volume. This EQ may be able to used on all tracks in the same buss as the reverb, depending on how you work.
Pull them down in the mix and mask them with either a synth pad or horns. Many times these techniques include some sort of other instrument(s) doubling the part.

Listen, adjust, take a break and listen again.



I do not work here, but the benefits are still awesome
Make your sound your own!