Here's another idea. Taking inspiration from Mortal Kombat X's Living Towers, what if SSF2 had a dynamic events mode with new challenges posted monthly, weekly, and daily. They wouldn't have to be that intuitive, just add a few of the Special Versus modifiers to you or your opponent not unlike the upcoming Peril Roulette in Classic mode.

Wow that sounds hype! Daily challenges lezzgo.

I was thinking of maybe there would be a mode called "Last Final Smash Mode" where when you get 100% or more and use a secret button combination, they can pull off huge reversals that will get anyone hyped. But, there are certain drawbacks.
- After the move ends, the character won't be able to use the Final Smash or any specials for the rest of the match.
- If you use it more than once, it will increase your percentage by 50%.
- Transformations like Hyper Sonic, Kurama Chakra Mode Naruto, Final Getsuga Tensho Ichigo, and SSGSS Goku requires increased percentage to maintain it so once it hits 0 you revert back to normal.
-Combo Final Smashes like Link's, Lloyd's, and Sora's will be even more spectacular with more ways to combo but if you want to use even more attacks, it will cost 5% per attack.

Well, to answer your question, wall jump.

Wall jumps arent even in this game And before you say Double Jump, its a common happening that you lose your Double Jump if you have to recover without specials. Like, almost 95% of the time. You are sentencing characters to die once they are offstage with a higher chance than Little Mac.

try walljumping in f*** clock town or dream land

Pure Salt Mode: You have to fight against the most voted characters that didn't make it into the game

SSF2: Chaos Edition

You and your opponents have random power-ups that change every 5-10 seconds.

Some ideas are:

slow
fast
2x power
unlimited jump
every move is a spike
insta-shield break
floaty gravity
moon jump
turbo mode
super armor
double cherry (from super mario 3d world)
super mushroom
mini mushroom
attack with 200x melee marth's grab range

Flight mode:Their is no stage, but the bottom wraps to the top.

This isn't really a mode in the traditional sense but SSF2 should have a debug mode like Project M to display hitboxes.

Only Combo Mode:

After 3 second of not being damaged, characters health will revert to 0%. Encourages combos and edgegaurding, as your opponent won't die unless you gimp them, or can chain your low knockback attacks and finish with a killing blow.

Interesting idea, but wouldn't that promote camping with Naruto?
Also going back to 0%... After 3 seconds.... Why not just heal like 5 or 10% every 3 seconds?

Melee Mode:

L-Cancelling, Melee Airdodge, Wavedashing, etc.

Basically, stuff plays like Melee

Fighter Maker:
Basically, a way to make/add your own custom fighters into the game. Something akin to Mii Fighters, except these are not limited to a set of moves. Think about it as some sort of developer tool, being able to import your own characters into the game, being able to make and edit their character's moves, hitboxes, taunts, victory poses, voice, sound effects, etc.
Basically, this mode would be similar to Mugen. This would allow for fans of the game being able to play as their favorite characters even if they didn't make it to the roster (ex: Being able to play as Ridley without people complaining about the game's roster since he would not be considered part of it) and the player not having to care so much about the character's sprites quality in comparison to the rest of the cast. Of course creating a character would take as much time and effort as the dev team.

tl:dr A mode where you can make and add your own Expansion characters.
This would come with some restricitions, though: not being usable on online play, and all of them sharing the same slot in the Character Selection Screen, kinda similar to how Smash 3DS handles the Mii Fighters and DLC characters into a separate menu. Also, this mode should be unlockable in the full game AFTER the player has unlocked all characters, so players don't cheat and add the unlockable characters right away

This would be a nice alternative to encourage people into being part of the game, and would discourage modders into making modifications to the game.