I mean, I would say*, don't worry about it too much. A pretttttty large amount of the actual mechanical parts of this game come from the pokemon. Although it's not true for all classes, for a lot of them it wouldn't really matter if there was some overlap. For example at least, my characters only thing that she does mechanically is give a few small buffs to my pokemon, even if your character was mechanically exactly the same as mine (well, a different type for the ace but whatever you get what I mean) so long as your pokemon was different it wouldn't really matter. That's not true for every character, like Weirdsounds for instance has some unique debuffs that he applies that doubling up on would be strange. But, especially since without the super natural classes some of the more unique options are not possible/less possible it seems like maybe it's not super worth worrying about too much. (Also this is especially true if the game goes on a long time and we get a lot of trainer levels, although I don't know what Birdys plans are for that direction...)
*Although I could probably be wrong.\
Edit: Here's sorta my impressions of what our party is right now, what we can do, and how important it is not to have the same features as that person. (Although of course, that is also pretty subjective to the person with the original character as well, weirdsounds might have the most important not to have the same features character, but maybe he would be perfectly fine with another roughneck for some reason, and I might have the most generic unimportant to not double up on features, and maybe I would care if there was another ace trainer. Well, I don't, but just as a example. So who knows.)
Pokemon:
Dog thing: Special attack dark with no Special attacks but some debuffs. Probably will get actual special attacks later
Eevee: Not going to try to predict that one... Okay, so... Defensive and special attack?
Abra: So, Psychic Special attack struggle attacks for now, Psychic special attacks later.
Squid thing: Physical attack dark with some debuffs and a nice buff and a very large attack
Fire thing: Special fire attacks. Maybe later some burn stuff, but that doesn't have synergy that well with anything but the fish thing
Trainers:
Juggler: Doesn't actually do that much now. Eventually will have some trickery with turn order and ability to have the right pokemon in the right situation, if this is a multipokemon game. A double wouldn't be great (simply because the effects are more interesting then some other classes effects), but wouldn't be totally awful ether.
Cook: Buffs/crafting I guess? Heals as well. A double would be sorta bad.
Survivalist/Under dog: Buffs to own pokemon. Some terrain stuff. This one really doesn't matter if there are doubles I don't think, especially if you have different terrains.
Mafioso: Debuffs I think? (Also can buff his own pokemon because of it's special ability? That's a cool trick if so) This one probably make the least sense to double out of everyone... Although even then it seems like most features have a choice of one effect or the other, so maybe even doubling it could be sufficiently different if you were careful.
Ace Trainer/Fire Ace: Buffs to own pokemon. Doesn't really matter if doubled. Especially so if you have a different type ace.
I find it interesting that four out of the five of us can debuff defense stages, ether though our pokemon or ourselves, but only one of us is really focused on physical attacks. (Although I guess Kansas pokemon is forced to physical attack for now)