i havnt listend to your example yet /no youtube acces right now
but getting that very polished and flawless vocals sound does indeed take some serious amount of work.
if you are willing to learn i suggest you to purchase those both online courses from creativelive.com , they cover really alot of important stuff that can help you out and inspire you in a great way
https://www.creativelive.com/courses/flawless-vocals-recording-editing-mixing-kris-crummett
https://www.creativelive.com/courses/recording-rock-guitars-andrew-wade
Basically, get it right at the source, so get awesome vocal takes to start with, and finetune it with melodyne, make the support vocal takes perfectly align and use vocalign for that.. it works amazing!
But please aware, if the performance itself is not good, it wont deliver, not matter what you are going to do with postprocessing.
izotope nectar is a nice programm but it harmonizing sounds pretty "synthetic" imho. what you can do is to yield more natural harmony is this:
when you have 3 tracks of main vocals tuned at original pitch
dont just use the 2 tracks of them to create harmonies, you need to use takes that you not have in your mix already, and pitch those up/down with melodyne.. that way it sounds way more natural and not as synthetic.
so then you basically need to record 5 great takes of those parts.. or even 7 takes if you want to have more harmonies, so your vocal group is going to consist of this:
1x Main Lead Vocal, panned Center
2x Main Lead Support Vocals, same pitch as lead vocal, pannend hard left and right or 80/80
2x or 4x harmony vocal tracks panned left and right to taste, pitch up or down with melodyne
compression and eq is another story.. gently reverb and delay also helps to sit them in the mix
tape saturation also works great sometimes..
i try not to overcompress, but sometimes lots of compression also does sound good.. so it depends, its always about to suit the recorded performance.
i really like to compress the support-lead vocal tracks alot so that they will not jump around as much and being more constant in volume.
and also i put a compressor with a fairly low compress rate on the vocal group-bus
i have the reverb and delays on aux send channels and set to 100% wet and not part of the vocal chain, so that i can always mix them to taste and dont need to care about other settings in the vocal chain, like compression..
hope that helps you at least to get an idea of it