I have 4 tracks that are exactly the same, except that each one has vocals in a different language. I know how to remove center-panned vocals, but is there any way to remove them that takes advantage of having multiple versions of the same track?
If the vocals are in different languages then no, there is nothing that can be done to cancel them out automatically.
If the different lyrics have gaps in different places then you could manually select these gaps using a DAW and drop them into a "master" version.
This may not be the answer you're looking for, but it may bring closer to what you want.
The idea is not to remove vocals, but reduce the volume: you simply put all the all the different versions on a track each in a multitrack program like Reaper, Cubase or Pro Tools. Make sure you precisely align the songs so the wave curves follow each other at sample level.
The outcome of this is that what is the same across the tracks, i.e. the music, is boosted and what differs, i.e. the vocals, is reduced. The more different versions you have the better.
If you wanted to remove the music instead, you simply duplicate the track which you want to isolate the vocals from, and phase invert that and increase the gain to the point where the average music from the four other tracks cancels out the music in the fifth track. You may need to route the four tracks to a group and reduce the volume of that instead of increasing the volume of the fifth as it may be hot already and cause clipping if you increase gain).