"Shifting the sound stage" is when you adjust the amount of each of the left/right channels and how much of each goes into the left/right playback channels. This changes the stereo image, effectively "moving" instruments around on the sound stage (what you'd imagine their positions to be if you listened carefully and visualized it).
Listen to some music with headphones on, close your eyes, focus and listen closely to each instrument. Now imagine that you're at a live performance at looking at the stage. The singer is right in the middle of the stage, and as you listen, you can hear the vocal are panned to dead center. Drums are often panned around the listener in the mix, so as you listen to the different drums in the kit, put yourself in the drummer's seat and listen carefully. The kick drum is likely panned to dead center, while other pieces in the drum kit are to the left or right.
As you continue to listen and imagine, you can hear and picture the bassist behind the lead singer. A single rhythm guitar may be panned close to center, or dual rhythm guitars may be panned more to the left and right. Keyboards are center panned, and perhaps there's a horn section somewhere on the stage.
As you visualize where the musicians are positioned on stage, think of them as "panned" to that location. Now, by "counter-panning" the left/right channels into each other properly, you can "move" the musicians around on the sound stage. So, for example, if a vocalist is panned slightly off to the right, then by mixing some of the right channel into the left, you can increase the amount of vocal removal. Effectively, you're "re-balancing" the mix.
Shifting the sound stage like this alters the entire mix though. So if you have a situation where there are 3 singers with one panned slightly left, one dead center, and the third panned slightly right, you cannot affect all three of them. You must choose which one you wish to affect to the greatest degree, then live with the results.
It's important to remember that you can only target 1 "position" in the mix, and that shifting the sound stage for that position will affect how well the vocal removal works for everything else as well.
When shifting the sound stage, you can also decrease the amount of vocal removal by re-balancing in the opposite direction.
For information about removing instruments from songs, please refer to Filtering Instruments from Songs.
Click here to download a free trial of Guitar & Drum Trainer and experiment with vocal removal for yourself.