I personally would love a King of the hill esque mode to be played with 2-8 players. It could be a way of ensuring some clear objectives in a 8 free for all madness. plus a great way of making big stages more interesting since it kinda nullifies extremely runaway tactics... The hill could be something complex, as areas of the stages, or something more simple like a platform that appears in random places in the stage.
Plus, since it should make big stages a little more interesting (since now you cant win by running away) maybe 3v3 and 4v4 (and to an extent 2v2, or even 2v2v2)could evolve into something akin to a popular meta. Oh, and walkoff stages shouldnt be that terrible since you cant neither camp the walkoff the whole match.
It would be also amazing if the stage maker got updated to enable stuff like setting where this king platforms spawn, setting multiple respawns (including team respawns) and the stage maker stages could be played on 8 man smash. right now is posible to create unplayable stages, so it shouldn't be a concern that people could create bad stages with stupid respawns.
And while we are at updating the stage builder, some Great cave offensive "Danger Zones" would be quite welcome to enable roofed stages, while we are at it, also some treadmills and some circular moving platforms please :3
As for single player? while a SSE adventure could be cool, i kinda prefer them devoting the resources to actual gameplay stuff. Still, and Adventure mode akin to melee would be amazing, reusing assets from the smash run, and creating new assets to do world themed stages (mushroom kingdom, zelda dungeon, fire emblem castle, donkey kong jungle, etc...)
Then those extra assets could be used for both the stage maker and character specific "break the targets" and "board the platforms"
Although a metroidvania style universe as someone posted above would be quite impressive, but it would require a lot of design work.
Finally, if we can ask for some Fluff, i would love to get tools to "beautify" stage builder stages, while it's perfectly possible to make very interesting functional stages, it's pretty hard actually to not make them look ugly as sin

.
I don't see an update of this proportion happening anytime soon though.. I got the feeling that they are putting all the resources into the 6 planned characters right now (which is quite ok in my book anyway, mewtwo, roy, lucas and ryu look gorgeous) and after those characters are done probably they will start pondering if keeping the DLC (I hope that they continue :D)