"that tight pop vocal harmony" is a little obscure….
Anyway you have different types of pitch shifting algorithms, from multishift to Diatonic shifter. Mulltishift can be used for fat doubling with a few +/- cents and short delay offset. This is the very popular Micropitch effect…check the preset with such name…great on vocals, snare, etc.. This algorithms can also be used to pitch shift a source by any amount of half steps (100 cent = a semitone) within the chromatic scale. The Diatonic Shifter will also calculate the correct pitch within the user selected scale and tonic, if you need in key harmonies.
The optimal settings require you use a monophonic input source, not a choir. And set the Low Note parameter to the lowest note you will pitch shift. For example a guitar lowest note is E2 or D2 for those intense whammy action solos.
As for delays…I'll leave the answer to those engineers…..
best
I
