I can't really say for sure as I have not read through all the media of this series. I don't know how this world works or what kind of nations and places actually might be outside of Orario. However, I couldn't help but notice that (with the exception of some of the xenos of course) all races in the Danmachi world resemble humans to a great deal. Like there is not a single character (except Fels), that doesn't look human. All the different races you'd expect in a fantasy world such as orcs, goblins, trolls, dragons etc. only exist within the dungeon as monsters. This might or might not be for fanservice like the genderswapping of certain deities like Loki or Hephaestus.

Perhaps it has something to with the christian belief of "god created man after his image", which also is strange as the gods also are completely human in appearance, but I got no confirmation for this thesis. So I'd presume with all we have seen thus far, that at least on the surface only races exist that are not to a large percentage inhuman in their appearance. The furthest as it gets is kemonomimi characters like Bete, Anya or Sanjouno with only minor animal features on them or other races like elves, dwarves and pallum, which can be distinguished from humans through their own unique traits.

To sum it up, I believe that everything within these lines seems to be possible at least from what we have seen thus far. If I had to name a species now, I'd probably say the Lizardfolk of the Death March series that Liza is part of or something like a race of oni-like humanoids. Or pretty much all the faunus characters from the RWBY series, that actually have animal traits unlike let's say Tukson or Ghira Belladonna. As long as the inhuman part is not too prominent like it is with harpies and mermaids, I guess everything is possible. Characters like Giselle from Gate might actually already be too inhuman for that world.