A lot depends on what sound you are after, the genre of music, how many singers, etc...

VERY generally speaking, the harmony would have to follow a fully edited (FINISHED) lead vocal track. Otherwise, they won't match. You can do one part at a time (doubling each part if you want a bigger sound). Then, spread them in the mix as you see fit.

If you are after an airy sound you can give them a gentle lift around 12-16k (during the mix). IN any case, make sure they don't interfere with main vocals if the track is such that there needs to be a clear separation between the lead singer and the harmony...which is not always the case.

There are too many options... :)

In dense set of harmonies, say 3 and 4 and 5 parts, I will break my rules about EQ at tracking and use it here. ESPECIALLY if the parts are going down one at a time. Mark this point.

CUT ONLY. Start with the lows and low mids. Find your feature instruments center frequencies and cut the backing vocals here. At tracking.

Unless its folk music and then these are the parts that anyone cares about anyway. So these stay upfront and thats all theres ever gonna be .....In this case, everyone gets a track of the most pristine and clear mic/pre/comp you can throw on it. Then you get to sort it out at the mix.....thats always a blast with 4 or 5 lead singers leaning over you......

This isn't the best way, but theirs not a best way to tracking anything.
It's just what works for what your recording at the time. But we were tracking rough tracks of a four part harmonie in my control room that ended up being the track's that were used at mix'n!

Tracked four vox all with close mic's and room mic. It set in the mix real well,

Peace...........Scoobie