Harmonizer Plug-In

Look here, a very good database:

https://www.audiopluginsforfree.com/?s=pitch

Pitchproof and Graillon are quite good in pitch-shifting. And there is also a very good harmonizer plugin by michael norris (part of his spectral suite). You can also create your own harmonizer with built-in logic plugins.

With some instances and in conjunction with a pitch-correction plugin, you can create matching harmonies which fit to your song.

And dont forget vocoders!

My personal favorites of the paid ones are eventide Quadravox (4-voices) and Octavox (8-voices). They are harmonizers with pitch-tracking and pitch-correction, you are able to choose from different tonal scales. And, independent delays per voice, this is where the fun begins. For sure, you can set all the delays to 0, so they work like a traditional harmonizer.

Pitch & harmoniser plugins tend to be some of the more expensive plugins out there... but you get what you pay for.

Here's a few of some of the best :

https://www.eventideaudio.com/products/plugins/harmonizer/h910-plugin

https://www.soundtoys.com/product/crystallizer/

https://www.antarestech.com/product/harmony-engine-evo/

https://www.celemony.com/en/melodyne/new-in-melodyne-5

Depending on whether you're just looking for just a harmoniser effect, or to actually construct (chord) harmonies, you can mimic the DNA behaviour of Melodyne using Logic's Flex Pitch - just on separate tracks. (You may need to offset a copied part, & use EQ to avoid phase issues).

I forgot to mention explicitly logic's evoc 20 as a vocoder via keyboard and vocal transformer via automation.

Good shout on Quadravox & Octavox (forgot about those, & have always wanted to give them a shot). Although I already have H3000, & a couple of others, I may need to add one of these to my collection...

To the OP... if we're talking vocals, there's no substitute for a great singer who can think & perform harmonically, but many of the above can be useful for more 'modern' vocal FX, or for working out harmonies.