Possible game modes:
FFA Arena/Deathmatch
Either match based or a continuous arena with changing maps (Nox).
CTF
Match based capture the flag, requires its own CTF maps.
Duel Arena (Wizard Wars)
1 vs. 1 with spectator area, the loser automatically leaves and a specatator can enter the arena to fight the winner.
Team Arena (like Battlerite) (2 vs. 2), (3 vs. 3), (5 vs. 5)
I'm not convinced team arena is a good fit. It's usually based on team balance and team counters. Although Nox has a few team synergies the gameplay is focused on the individual.
Battle Royale / Last man standing
Battle Royale is basically just last man standing with item hunting mixed in on a big map. Item hunting is already a part of the game anyway so a large Nox LMS would be considered BR i guess. Fits very naturally and BR would also allow for fun campaign-like overpowered items to spawn.
Dominion/Conquest/Point capture (team vs team)
Capture points generate points, they also spawn mobs. Accumulate a certain amount of points to win.
PvE
A small co-op survival mode would be realistic, quest style would be nice but the development time required is too high i'm afraid.
Others:
King of the Hill
Search and Destroy(Rush) (Requires special maps)