Multiplayer Mode

Multiplayer Mode was a scrapped game mode for Super Mario 64 that went through several changes until being removed entirely. This game mode would have been where Luigi would have been played as before Multiplayer Mode was scrapped as well as Luigi by extension. Multiplayer Mode was scrapped mainly due to technical limitations, and also due to the Nintendo 64 not coming with a second controller.

Description
Multiplayer Mode, in all versions, only consisted of 2 players, who would play as Mario and Luigi. It originally would have played like the standard game with the added character of Luigi, though technical limitations prevented the game from having both elaborate levels and Luigi. Eventually, a new Multiplayer Mode was devised that would have had a minigame that would have played similarly to the first Super Mario Bros. game, though due to the Nintendo 64 coming with a single controller, Multiplayer Mode was scrapped in it's entirety.

Multiplayer Mode returned in Super Mario 64 DS with playable Yoshis. Various smaller levels can be played in Multiplayer Mode, as well as several of the minigames that can be found in regular gameplay. This Multiplayer Mode appears to be similar to both versions of the Multiplayer Mode from the original Super Mario 64, having regular levels playable as well as minigames of some sort. It is not entirely known if this was simply a coincidence, or that this Multiplayer Mode was loosely based off of the original Multiplayer Mode.

Super Mario 64 Reimplementation
Perhaps one of the rarest and unstable anomalies known to be created by the Personalization A.I. is the re-implementation of Multiplayer Mode into the game. It can appear as either planned versions of Multiplayer Mode, with the Super Mario Bros. version most commonly manifesting in an anomaly known as The New Mario Bros. However, the first incarnation of Multiplayer Mode is more common than this minigame manifestation.

The Multiplayer Mode's non-minigame manifestation has several inconsistencies in reports. Some claim it has new playable characters besides Luigi and Yoshi, such as Wario, though many of these reports are unconfirmed. Some reporters claim Multiplayer Mode has split-screen for each player, some claim it does not. Some say that Multiplayer Mode has to be unlocked, others say it is accessible from the start of the game, which is strange due to personalization relying on the player playing the game. However, several have claimed that entering the same room or area with both players if they start in different locations can cause significant amounts of corruption, or the game crashing, potentially due to the instability of Multiplayer Mode's reimplementation.

The second playable character has been reported to be much more glitchy when moving. Some have claimed they occasionally refuse to move before abruptly being playable again, that the controls are warped, or that they will occasionally suddenly lose or gain speed while moving, and similarly, either suddenly gain or lose height while jumping.

Theorizing
It is believed that Multiplayer Mode is generally inconsistent and unstable due to the scope of the reimplementation and technical limitations, similarly to the reason behind the removal of Multiplayer Mode in the first place. However, the fact that Multiplayer Mode can potentially be reimplemented appears to question this as some have reported it to be fully functional without any additions to the cartridge or console.

Alternatively, some believe that the Personalization A.I. is reviving the mechanics from the minigame version of Multiplayer Mode though, instead of putting them in the minigame that isn't reimplemented, places them in the main game. This may also explain the instability due to the Multiplayer Mode being out of place and incorrectly adapted to the main game by the A.I.

Greenio's Documentation
In Greenio's video "multiplayer-test.mp4" that appears to be testing of the Multiplayer Mode mechanic. Mario begins in the Castle Grounds, and Luigi appears to begin in the Castle Courtyard. Both players explore their starting areas, before Mario enters Princess Peach's Castle and continues looking around. Luigi enters the castle, but the moment they enter the main room, where Mario also is, the game appears to freeze and then crash. Notably, this crash appears to be similar to one of the many issues reported with Multiplayer Mode when it is reimplemented.

Report 1
"Oh yeah, multiplayer mode. I tried it like one time for three minutes but when it broke, I just moved on because it wasn't the only thing that got broken. So, I didn't actually have anyone else to play with me, because this is like decade-old technology, and I just wanted to see if this thing worked. So, Mario started in the Castle Gounds, but Luigi started inside of the castle. I thought that was weird. I messed around with both, making sure everything worked fine, which it did, until I took Mario into the castle. BOOM. Crashed. I just gave up and went back to my 121-star save to see if I missed anything, since there was like 50 things I didn't do yet."