Different preset for new version (background) of duplicated vocal track (melody)

I’d like my background vocal track(s) to have a different factory preset than the melody from which they were copied. Is this possible, and how do I do this?
Using factory VariAudio/VocalChain

If you create a new track for them you have full control over the preset and additional plugins you want to employ.

Not enough info. I duplicate the track. I shift the notes which prompts a new version. When I select the new track and select a new preset, the preset changes for both tracks: the duplicate and the original.

Not enough info. Which preset are you talking about? Maybe a screenshot would help.

Any of the ones in the dropdown.

I have never seen such a thing. No idea why that happens on your side.

Have you selected “Link” and included inserts? That will link the parameters between inserts for all linked channels.