Ever since Brawl, the Super Smash Bros. franchise has not been a wholly first-party affair. It in that game that the first third-party characters were introduced in Solid Snake and Sonic. Smash 4 upped the ante with even more characters, ranging from Pac-man to Cloud. In a reboot, they would not all be cut out of the roster, as Nintendo did not forge its history alone.
The first of these supporting characters in the lineup is Mega Man. His series dates all the way back to 1987, and of the mainline series, only Mega Man 8 did not originally release on a Nintendo system. Needless to say, he is as close to Nintendo as third parties come, and a long time veteran like him deserves to keep a slot in this roster. His current moves show great faithfulness to the series, though he could probably stand to have some representation of his upcoming game added.
Mega Man's stage would draw from another part of the series: Mega Man X. Being based off of the opening stage from the game of the same name, it would be a somewhat flat stage, that breaks apart as the fight progresses, and eventually it would reset itself...somehow.
This next one would come with a condition. Sonic the Hedgehog was an important part of Nintendo's history, but mostly as the flagship for one of Nintendo's earliest competitors: Sega. If Sonic were to be included, I would give him a rivalry with Mario to reflect their console wars. This would probably be accomplished through the Adventure mode and some victorious taunts after multiplayer matches between the two. Concerning the actual gameplay, his moves could be diversified, but without doing much research I can't really go into specifics.
For a new Sonic stage, Starlight Zone would give a stage with rolling hills and an overall interesting layout. Throw in some sea-saws from that level, and you have a neat stage!
A more recent third-party that has earned a spot would be Bayonetta. While she may not be that impactful, she is still practically a Nintendo character at this point, with Bayonetta 2 being exclusive to Wii U and later Switch, and the third game in the series is going to be exclusive to the Switch. Her games also bear the distinction of being M rated, something almost nonexistent among Nintendo exclusives. As for her stage, I am completely unfamiliar with the series, so I have no ideas. You know the drill: if you give an idea in the comments within the week, it will be featured.
These are all returning characters, but what about a new one? Well, Nintendo (and the Switch in particular) does a great job of supporting indies, so it would be fair that they as a whole get some representation. While there are many great indie games that could reasonably take the slot, Shovel Knight would be a solid pick, due to his popularity and Yacht Club's close relations with Nintendo. His move set would consist of mostly shovel fighting for tilts and aerials, with the down air being his signature shovel pogo, which lasts until he either lands, takes damage, or uses another attack. His specials would employ his relics, with the Flare Wand for the neutral, the Dust Knuckles for the side, the Throwing Anchor for the down, and the Amiibo-exclusive Rising Dagger for recovery. His final smash, which could be referred to as Treasure Trove, would call in the other playable characters (and Shield Knight, of course) to aid Shovel Knight in battle. While Shovel Knight himself would only experience some decent stat buffs, he would effectively have four assist trophies supporting him.
Shovel Knight's stage could be based off the battle in the Tower of Fate. The stage would start off flat, but the entire stage is destructible. If parts of the stage get too damaged, it would be rebuilt through fire. Perhaps even the Enchantress herself could appear as a stage boss.
With that, the roster of my rebooted Super Smash Bros. is complete. To be honest, I set a personal goal to complete this series before Nintendo's E3 presentation, and I am glad that I met it. Speaking of that direct, it is tomorrow, and an actual Super Smash bros will be there, so let's get excited.
Read the previous parts:
Part 2 - Mario Adjacent Franchises
Part 7 - Pokémon and Metroid Stages
Part 9 - Now-One-Off Franchises