It's been said before, but maybe not stressed enough... One PC non-human is easily doable. Multiple from different races isn't likely to last long as a campaign. There is, after all, a good reason everyone isn't all living in harmony. The "common enemy", IMHO, gets boring pretty quick... And doesn't justify a long existence for the group.
But... IIRC, the Wooden Sword had to be returned to the elves to be used properly. So, there is Humakt - a cult that can be worshipped by humans, ducks, elves, and the rare troll. If Humakt gave them all a mission, they'd be forced to work together (but probably not happily). We could also argue that joining Humakt not only severs family and cult ties, but also racial.
The PCs could be the beginning of an attempt to reform the Elder Council. (Could just be a vision they've all shared)
Something has gone wrong with Dragonewt reincarnation, and their souls are ending up in strange bodies.. and worse, taking on weird personality defects.
Or, similarly, Belintar's soul has fractured into these different PCs.
A Trickster told a Lie to them that they were all good friends (in the middle of a 5-way battle over a sacred/magical object??)
Fate has played a tricksy hand... They'd all sworn a weird oath (along the lines of "the next person who...") and has twisted them together. (Sort of like the Witcher's unexpected surprise thing).
The bigger question will be... Can the players RP it properly? In LotR, the dwarves and elves were supposed to have this serious mistrust and almost hatred of each other. Certainly continual suspicion. However, Legolas and Gimli were really boring. I.e., they didn't play their characters well. (Reminds me of Star Trek and other scI-fi with similar plots). Or D&D, where Paladins happily hang around with the CE assassin, long after they should....