For what its worth, in a Mamas & Papas video biography some years
back they talked about a "ghost voice" they heard when they
all sang together (Denny said they had a name for the voice, but
I forget: Larry?). And I recall reading about the Hollies saying
something similaqr, and they all sang into a single mic (at least in
the early days).

You probably don't get that with separate vocal tracks.

Some friends of mine in a band featuring close harmonies describe a "ball
of
sound" that forms in the air when the three of them are singing just
right.

Back in the middle ages, when instrumentalists did this, the extra voices
would come out of the cathedral ceiling. The musicians called them
"angels".

Last I checked, evoking supernatural voices wasn't part of the job
description... stick to what works.