A bigger single player, more customization options, new weapons/maps of course (especially more content at launch) and some small tweaks to make the MP fresh. It doesn't need much really.

I would like to see players vs coms like Mann vs Machine type mode in Team Fortress 2

Local Multiplayer for single player would make sense too

:-O

Inkling survivor mode. Think Splatoon meets Call of Duty zombies. 1 to 4 inklings team up and fight against icreasingly tougher octarians, but as you progress, you can upgrade your inkling and your weapons (using a sort of combo of the single player upgrade system and the multiplayer weapon and perk system).

A more extensive single player, and maybe more multiplayer modes and options.

Additions like integrating the Splatoon website, adding a spectator mode, or having LAN mode would be very nice features as well.

A storyline for the Inklings and another one for the Octolings, showing both sides of the war.

I do not see any way that Splatoon does not get a sequel. It was a huge success for Nintendo

Voice chat.

(Yes I had to be that guy.)

i expect hardcore modes for sure

1-only vertical turf claimable levels;
2-randomly generated invisible paths inside the levels (I think it's possible and it would be amazink);
3-3 or even more teams turf wars;
3.5- stages mirrored for all the 3 or more teams;
4-races in randomly generated levels that you have to take at the same time as your opponents, the first that reaches the zapfish wins;
4.5-^same but with teammates that try to hinder the progress of your opponent;
5-Voice Chat;
6-totally new sistem of stat boost;
7-ink skateboards and roller skates (in collaboration with SEGA for obvious reasons)

I can go on, please Nintendo hire me :c

Honestly, I think it would be cool if online only games just added DLC content over time. This probably won't happen, but if they were to do that, it would be better than a sequel in my opinion. This applies to any online only game.