Theoretically it's possible on the PC version. It depends on the encounter group, though. Here's a list of things that one would need to do:
1. Add the battle background to the battle.lgp file. The last prefix there is sm__ (Vincent's Chaos) so you'd have to use files sn__ - zz__ for any additional backgrounds. That's a lot of potential there.
2. Create encounter groups for these exclusive battles. There's only a limited number of these available. You might have to use some dummied scenes for this. Proud Clod will do this easily (at least, as easily as possible)
2a. Within these new encounter groups, you'll need to change the background value for them in Proud Clod. The new values would be 6Fh - 131h, depending on the file prefix you used.
3. You'll have to change the field files to allow for the new encounter formations in these locations. I'm not sure how to do this. I think Meteor can do this. There might be another that claims to do this too. The absolute formation index value is
explained here.
This is just theoretical. I'm not entirely sure how the PC decides which files to use, but I think it's sole based on the value of the background since it's not directly indexed.
It's likely impossible on the PSX version to insert new battle backgrpunds, but you can still change around encounters and formation backgrounds.