Off the top of my head (with the big-flashing-angry-red-letters caveat that I've not played with these parts of Essentials and so don't know how well it'd actually work), I wonder if it would be possible to:
1. Change the maximum possible IV to 32
2. Ensure that pokémon can still only be randomly generated with IVs ranging from 0–31
3. Create a new characteristic that only applies when all IVs are 32 (or when only a certain IV is 32, allowing you to create up to 6 new characteristics)
4. When you want to give a pokémon with the new characteristic to the player, manually assign it one or more IVs of 32, as appropriate
It sounds simple, at least, and would give you the added benefit of letting these "special characteristic" pokémon have something else special about them (slightly higher stats than normal). But again, I don't know that it would
actually be simple, because I haven't looked at this part of the code at all. Maybe the IV range is more tightly tied to personality values than that, or maybe futzing with the IV range will affect something else I haven't thought of. I know the general idea behind how characteristics work in the games, but I don't know how Essentials implemented them and they may not be that trivial to alter. I would
guess that these changes would be all right, but I don't
know, so someone with a better understanding of the relevant code will have to weigh in, or you can check for yourself.
I also don't know whether you want to bother changing the way IVs work at all, or whether you want these special characteristics to tie in with stronger pokémon, so even if it's possible this may not be what you're looking for. It would help if you explained what you're trying to accomplish with this new characteristic, and/or why it needs to be the characteristic that is different. Maybe there's another way to achieve your desired result without messing with IVs at all.
EDIT: Although, really, I'd be surprised if it's truly
impossible to just force a characteristic based on some other criteria. Maybe you could create some sort of special attribute that can be set for a pokémon, a simple boolean option or whatever, and then tuck the code that decides the characteristic into an if condition. In grossly-oversimplified pseudocode, something like
Code:
if specialAttribute = 1
characteristic is "This characteristic is fancy and special."'
elsif specialAttribute = 0
characteristic is "code to generate characteristics normally goes here"
end
But that would require defining said new attribute for all pokémon, and so forth. Something like the way shinies are defined, perhaps, but affecting far fewer things (unless you wanted it to do something else as well). Again, I couldn't even begin to tell you exactly how to do that, but it definitely
sounds possible to me. I leave it to you/someone else who knows Essentials better than I do to actually work it out.