On commercial records, it's common to triple-track each harmony part.
Left/Center/Right
So a three part harmony would have 9 "singers".
This is how the part sounds lush/dense... and takes on more of a "group" sound rather than hearing the individual takes.
You'll not achieve this effect any other way than doing true double/triple tracking of parts.
Auto doubling (via pitch/delay) can sound nice... but it won't get you that super complex/animated result.
It's the small differences in each take that really animates the combination (especially as the parts are spread out between left/right). If you run auto-doubling EFX, the result is a LOT more homogenized.
Ambience can certainly add a sense of depth/space... but it alone won't take a vocal track and make it sound like a group of singers.