I've always been an enthusiast when it comes to Progressive genres, but one aspect of all rock genres seems to really interest me: multi-layered vocals.

It was this reason that I fell in love with Spock's Beard, because of their integrated use of the technique.

Does anyone have any good Progressive bands that utilize this technique?

The best example other than Spock's Beard is at the end of Black Water-Doobie Brothers.
Play the man, Master Ridley; we shall this day light such a candle, by God's grace, in England, as I trust shall never be put out.
Try Yes.
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I ain't dissin' ya bro.

I be doin' some 'o dat sarcasm **** right thurr.