I already have two games for Wii U, splatoon (which I believe to be only 2 player, I've not really looked into it) and mk8 which is obviously good as a multiplayer. However, I'm looking for more games that are good multiplayer games that do not get too repetitive (so basically with some sort of story or progression) as it's the same three people I play with. I did see trine in the estore which would have been perfect but it's only up to three players which wouldn't work out
If anyone has any good suggestions I'd be very grateful!
I can't recommend Super Mario 3D World enough. It's one of the best Wii U games out there and also supports four players. New Super Mario Bros U is also four players. You probably won't find much in the way of four player games with a story. Smash is always great for multiple people, and there are plenty with two players like Donkey Kong Country: Tropical Freeze and Yoshi's Woolly World if you don't mind just switching out players.
Splatoon only supports two players locally in a very limited multiplayer mode, but it is intended more so to be an online game. Truth be told, you're not really likely to find much in the way of a four-player game that offers a story, at least not without repetition of some sort.
The gameplay for New Super Mario Bros. U, Super Mario 3D World, Rayman Legends, and New Super Luigi U is identical regardless of if you're playing with one person or four. Other games you could consider with multiplayer are Tekken Tag Tournament 2: Wii U Edition, which supports up to four players broken into two teams of two, Kirby and The Rainbow Curse, which allows for four players to work together, Nintendo Land, Sonic & All-Stars Racing Transformed, The Wonderful 101, and Mario Party 10, which allow up to five players, Super Smash Bros. for Wii U, which allows up to eight players, and Runbow, which allows up to nine players. Sometime next year, Disney Infinity 3.0 will introduce the first four-player local multiplayer game mode, currently titled Marvel Battlegrounds. All currently known Marvel Disney Infinity figures will be compatible with the game mode.