Super Mario 64 had multiplayer at one point but the N64 couldnt handle it
New Super Mario Bros Wii isnt the first time Nintendo tried multiplayer in a Mario game
New Super Mario Bros Wii is the first multiplayer Mario platformer, but Miyamoto has revealed in the latest Iwata Asks feature that Mario 64 originally had some multiplayer action as well.
Super Mario 64 at one point had a split screen multiplayer mode that had Mario and Luigi entering the castle at different points but there was also a mode where "the camera is fixed and we see Mario running away, steadily getting smaller and smaller". This mode was a remnant of a mode where you could run away from each other but still see both.
Miyamoto attributes the Wii’s processing power to finally able to get a multiplayer Mario game up and running saying "The CPU is much faster than anything we’ve worked with before, its graphical capabilities are advanced and it has a large amount of memory.”
Iwata asked "So your longstanding dream has finally been realized on Wii?" Miyamoto said yes. Mario 64 DS had multiplayer but in a strictly competitive sense, it also wasn’t on a home console.
Source: Iwata Asks