AKA how everyone arrives in the game/what the heck they're doing here. General consensus I've seen so far is to keep the current flexibility of a nexus setting with optional jamjarring. For the sake of covering all the bases, I'm just going to throw every idea in here that I can. We can mix and match ideas, but let's talk about what you'd like to see in a premise for Smash Bros themed Floating Island Adventures.

A) The character trophies (per the ones in the basement/bunkers) are actually something of a spirit totem and have pulled characters from their respective universes to this Smash Bros 'verse to (fulfill a personal quest, mission or goal/x amount of time has past/fill in the blank) before they are able to return back to their home world (This is a "jamjar at first then freedom of nexus" option). Maybe they can go to other character's worlds in the meantime but not their own?

B) Characters come willingly or randomly, similar to the current premise; your character has heard of a mysterious floating island where tournaments take place and they can win exorbitant prizes, or get a wish fulfilled, or come on the promise of "finding strength", or have bragging rights, or whatever... or jamjar gods warped them in because a wizard did it. If the latter they are "free to leave" at anytime, at mun's discretion. (In other words, it will be entirely up to you to decide why your character is here and how they got here and what places they have access to and when.)

C) This universe is something akin to Brofist TV where characters pulled in are already known of and seen as celebrities (whether they realize it or not) by the local natives in FDC. The mansion is where the fighters reside and a separate island is where a huge colosseum-styled stadium (bigger than the current one) they fight (or hack-fight or have bake-off competitions or race) annually/bi-annually/quarterly and the natives come to place bets and cheer on their favorite fighters in probably a totally cheeky way that teeters on the 4th wall. natives are muns of the game in the game ok no. Prizes and rewards (trips home? wishes granted? money? bragging rights? personal strength? see option B) await the winner.

D) Master Hand is actually a malevolent child disembodied floating hand looking to collect cool "toys" for his amusement to do at his whim (see original Smash Bros) and send back to their respective worlds when he gets bored. This would really only work as a pure jam-jar set up.

E) Your character is made aware they are from a video game and they don't actually exist. Surprise, enjoy your existential crisis and then your time doing whatever you want to do and blaming everything on "game mechanics". no lets not do this