So there is something that I got to ask
Do you guys think that after Ultimate, it will be time for Smash to evolve from 4 Special Moves to 8 Special Moves?
Brawl was really the last game that added to the General Moveset of characters, with the Final Smash, and if the Future of Smash Will still use the General framework of the Series so far (in that it's not a reboot), adding more Specials universally would be a Good addition to add Freshness to the general gameplay that's been a thing for over 20 years
I also think it would be a really good compromise for people that like the Current Movesets of the charcaters, and people who want the movesets to be changed in certain ways. Ganondorf would be a good example, as Another Set of Specials would allow him to stuff like Float, Dead Man Volley, Reflect, Trident, Ground Pound, which would make him feel more complete
Of course not every character has enough material for another set of Specials, so perhaps some of the moves could be EX Specials, which might have meter used tied to it
Balancing would be something to take into account with more moves, and certain additions to certain movesets would drastically change how certain characters can be played, but Sakurai did say that Fun was priority over Balance. The addition of 4 more Specials might make Smash more of a Hyper Fighter than currently, but if it needs to be done, so be it
If we going by Joycon standards (which has 6 Buttons), 5 would be used for general actions in the game (Jump, Attack, Special, Shield, Grab) which leaves an extra button open that could be used for a 2nd Special Button
I think just another Special Move button would be confusing. Even fighting games with more buttons have a clear distinction between them such as light vs. medium vs. heavy and punch vs. kick. However, I do think an EX system could work.
My idea for an EX. system in this game would be similar to the V-Trigger system from Street Fighter V (though, perhaps only at a surface level). Each character would have about 1-5 EX bars depending on the character and how many is too many or too few. The average would probably be 3. Once you gain a bar, you can use that to perform an EX move with what's currently the 2nd jump button, which will be a stronger version of a Special Move. Sometimes these will simply be named EX [MOVE] but some characters will have their moves be called something else (ex. Thunder Jolt becomes Thunderbolt and PK Fire becomes PK Fire γ). If a character fills up all three of their EX bars, they get access to a Super Special Move (or something with a better name), which is initiated by pressing the EX move button and the Special Move Button. Super Special Moves aren't the same thing as Final Smashes, but they are still super moves at a lower scale.
This system has an added benefit that you were looking for as well in that it can give characters access to moves that they should be able to access, but don't fit anywhere in their kit, such as Roy's EX Flare Blade becoming his projectile attack, or Lucas's Super Special Move being PK Love.
What's even cooler is that some characters could modify or substitute the system with something else. For example, Min Min gets a Rush Gauge instead of an EX one, which differs in that it allows her to fire large lasers from her Dragon ARM, fire her Ram Ram ARM at a rapid rate, and super power her Megawatt ARM, but also forces her to plant her feet during the move. Essentially, she only gets a Super Special Move, but it's on the more powerful end.
For an example of something much different, Mega Man could forgo the EX gauge in favor of the Double Gear System. Left EX is the Power Gear, which powers up his attacks (and potentially increases the damage he takes, but that's a balancing thing), while Right EX is the Speed Gear, which ups Mega Man's speed. Using either gear fills up a heat gauge, that deactivates your gears, and lowers some of your stats when it fills up. When MegaMan reaches 100%, he can use his Super Special Move: Double Gear, which does both at the same time, but unlike either individual gear, it can't be canceled, and the overheat causes stronger detrimental effects; it is a last resort only.
What certain EX moves would do and how characters that already kind of have this system (Cloud and Joker) would interact with it I dunno, but I think it could be a really good system.