It's always good to get someone else's voice in there, even if they're not a good singer. You're trying to assemble a rich mix of overtones and formants, which is next to impossible when it's the same voice doing every part.
When my granddaughters were 11 and 12, I recorded them singing some oohs. They were shy so it took a lot of prodding to convince them to do it. But after tuning and treating the tracks, they sounded like a choir of angels and were pleased with themselves. I had them each sing the same notes of the triad, six tracks in total, each treated and panned differently. It's similar to the technique used on Bohemian Rhapsody, which had three takes of three singers, who swapped each others' parts for each take.
I'd read of the same technique being used to create a violin section with one violinist. They set up four chairs, which he rotated between while overdubbing the parts. Why not just pan each part? Because when it's acoustical instruments, it's not just about panning; the room sound is different from one position to the next.
Which makes me wonder if the same trick might not work for vocals. Not necessarily moving around the room, which wouldn't help since you're probably recording in some kind of dead space. But you could vary the distance and angle from the microphone for each pass, or even change out the microphone, thus getting a unique tone for each take.