vocal layering...how to do?

[Lvanett]

Can anyone give some tips on how to create vocal layering, creating a "digital choir"?

I'm not sure what to use with (currently am using audacity). I know there's a way, or so I've heard, to duplicate a track with one person (or more) singing, then tweak it just enough to make it sound different, then repeat the process. I'm working on singing background vocals to some material for fun and was wondering how to do this? The only way I know how is to record the vocal over the music, save as a new file, then repeat the process. This leaves the music and vocals sounding not as neat and smooth as possible, and leaves no room for error.

Help!

Thanx