Vocal Layering

I've always wanted to try the Bowie "Heroes" technique, but don't record in a room big enough:
 
Set up a close mic in front of where you'll be singing.
Set up a mic farther away, and put a noise gate on the input so it only picks up the voice when it's sung louder.
Set up a mic at the far end of the room, and put a noise gate on the input so it only picks up the voice when it's sung loudest.
This way, as the vocal performance changed from quiet to almost shouted, more mics came in and re-shaped the sound.

The way I do this is similar to what has already been discussed.
 
I record the lead vocal on several tracks. Each one is a unique recording take. The goal here is to get the phrasing, pitch, and timing as close to exact as possible.  For example, you want all the "S's" to end together, and start at the same time. Leave nothing hanging out there on it's own. Those "S" sounds tend to cut through clearly and will be heard.  You do the same thing with the harmony tracks.
 
How many tracks you record is up to you. I tend to do at least 5 for a minimum. One lead, 2 layered leads, and two harmonies. I take the time to work through each track using Melodyne to fix the pitch and timing issues.

Mixing:  I run the main lead up the center and at the proper level for the lead vocal in the song. The layered leads are panned to the sides and are at -10dB or more.  Generally, I don't really want to be able to hear them in the mix. Hit the solo for the vocal buss and you should be able to hear the layered lead tracks. If you record 4 lead vocal layers, pan 2 R and 2 L and put them at different positions..... one at 50% and the other at 100% for example balanced on both sides. Experiment with levels and position.
 
Do a similar thing for the harmonies. Unless you are looking for a Statler Brothers vocal harmony where each harmony voice is clearly audible, keep the harmonies down low like the layered lead vox. Bring them in enough to provide the harmony spot without it sounding like a group of singers in there. I like to get that level to the point where the harmony is evident but not something that the casual listener instantly hears. It sounds good but they can't tell you why.  You hear this on many of the hit records.
 
Since it is the lead singer's voice and not other singers, it simply adds a fullness to the lead vocal or a thicker sound.
 
That's how I tend to work my vocal tracks in the songs I record.

If you're looking for a chorus of voices, rather than just layered subtle vocals and harmonies, using Melodyne and playing with the formants might get you where you want.  A better alternative is to find a few people interested in helping with the vocal chores and tap their time and talents for the projects that need vocal group singing and harmonies. In another forum site I tend to hang out in, there are vocal collaborations on projects quite often. I've been in a few. Someone sends me a rough file and I lay my equally rough vocal on it and send them back a raw wave. They do the hard work on their mixing process. There are both male and female vocalists doing this. Most requests come in the form of a PM asking if the person is interested in helping out. The downside is that the project time schedule depends on others getting the recording done and back to you in a timely manner. The upside is, it doesn't sound like you sang it all with formant artifacts on display.
 
Edit: one more thing... I hesitate to even suggest this.... the Vocaloid singers are getting better. Some of them excel at certain genres of music and some of them are decent as background singers as long as they are low in the mix and not the lead singer. That gets you a female singer that is on call any time you need.   (proceed with caution) Personally, I don't have one and probably never will.
 
Just my 2 cents. Hope this helps.