As far as third party newcomers go, I already mentioned
Rayman a few pages back, so there's him.
I feel like
Shovel Knight would be cool to see. Not sure if he's too new (though Bayonetta making it into Smash seems to cut down on that being as big of a factor when it comes to third parties), but there's definitely a lot of material to work with for him, and there seems to be a lot of mutual support between Nintendo and Yacht Club Games (between the amiibo, Shovel Knight expansions launching early on Nintendo consoles, and Shovel Knight being a consistent fixture for being featured on the eShop).
As far as a second Namco-Bandai character goes, I'd like to see
Heihachi Mishima or
Agumon; Heihachi for the unique nature of a villain being the face of a third party series (on top of having a noteworthy design and his abilities being a contrast to Ryu's), and Agumon so we can officially have Pokemon vs. Digimon.
If Snake comes back, it would be great if they could get
Bomberman as well, though if I had to pick one, it would be Snake.
Part of me wants to see
Doomguy, given that (much like Ryu and Cloud) he's arguably the face of an entire genre (or at least the most noteworthy one that Nintendo could actually use, given that Master Chief's obviously a Microsoft character and Call of Duty doesn't have any immediately recognizable protagonists), but between first person shooters not being big in Japan, Bethesda/Id Software only putting games on Nintendo consoles recently, and the fact that Doom is so heavy on the gore, it will never happen.
Ryu Hayabusa seems like a definite possibility, given that Koei Tecmo has been trusted with spin-offs for two major Nintendo franchises (Zelda and Fire Emblem), and Ninja Gaiden has a long history with Nintendo consoles.
I really want to see
Travis Touchdown. Suda51
still wants to see
Travis in Smash, and with No More Heroes 3 coming to the Switch, maybe it could happen? Sure, the No More Heroes series is certainly heavy on mature content, but a lot of it shouldn't be an issue in Smash (cursing doesn't matter because they barely talk; blood in the NMH games only really comes into play during finishing moves and cutscenes, so that seems easy enough to work around), and I thought the same about Bayonetta (would have loved to see her in Smash, but the mature themes and relative obscurity of the series made me think it was a pipe dream), and that worked out.