More online modes, like 4 teams of 2 at once (doing some kind of minigame that could work for 4 teams of 2)
Wave mode (having to work together with other players to defeat increasingly difficult NPC enemies that increase in difficulty)
Make super sea snails easier to get, please, maybe 1 for every 10 wins instead of 30
More customizable private battles, getting to pick things like the ink colors, map music, even time of day (so you can play night stages whenever you want, maybe even morning or sunset stage times too)
Coming off what I just said, maybe every rotation features a time of day change too, since it's a game played around the world a game clock would be kind of messed up since some places would have day and some would have night maps, which could be an advantage or disadvantage, so maybe every rotation the time of day changes for a greater variety and maybe make the world a little more realistic.
I would also like to see a bigger plaza or area to walk around, maybe even the option to go online and walk around the plaza with other players, although I doubt that would work. Just a bigger non-gameplay world would be more fun, with things like mini-missions to get you extra cash o exclusive items.
Also a story mode more akin to Super Mario Galaxy with longer levels and multiple goals, and EASTER EGGS EVERYWHERE come on Nintendo it's what you do best let's throw in as many references and 4th wall breaks as possible.