
1 - The art style
First of all, they need to give the franchise a new style. The original's artstyle was quite bland and the realistic + cartoony characters didn't mesh well at all, leaving the aesthetics to be pretty unpleasing at times. To combat this glaring problem, design the game around a 2D cartoony style, like Guilty Gear or Blazblue, or even make it 3D cel shaded, like Street Fighter IV/V, where all the characters stick to one dsitinctive style. I think the former would work well, as characters such as Ellie and Joel, Nate, Kratos etc would look cool in a 2D style, and of course, would blend much better with the already cartoony roaster, which includes the likes of Jak, Ratchet and Parappa.
2 - 1st party franchises
Make more character playable from single IPs. instead of just Sly Cooper, have Bentley and Murray too. Joel and Ellie could work well as a duo set of characters, but the likes of Daxter and Clank, who have had their own spin offs, could work well, separated from their respective partners. Daxter could utilize his gadgets from his PSP game, and Clank could use his Secret agent tools, as well as his time shifting powers from ACIT.
3- Only add relevant 3rd party characters
Remove Raiden, Big Daddy, DMC Dante - these characters are not what come to mind when one thinks of Playstation. Replace them with 3rd party characters that people identify with the Playstation brand. Crash and Spyro are must haves, since their original PS1 titles will always be PS exclusive, and will always be associated with being original mascots for Playstation
4 - Remove the Super System
Make it more like a traditional fighter. The super system got old fast, felt cheap, and overall was fairly unbalanced. The characters should have some sort of health bar, but Supers can be altered to act more like ultra combos from Street fighter, where they are effective, but not mandatory.
I'd love another one of these on PS4. Playstation boasts an awesome roster of characters - it would be a waste not to have another go at this IP in the near future.

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I agree with everything to a point. I don't want it to be a traditional fighter. Just full-on copy Smash rather than the 90% they did before.
Just hire Nintendo to do it for them.
The Supers is what killed it for me. Just let me put enough damage into them so I can blast them off the stage.
For a Super there should be a PS logo sphere hovering around and if you get it you get a Super
Make it a 3d brawler unlike anything we've ever seen before. every body gets a 3rd person view make the stages big and ICONIC but multilayered and not just one big open space but ad some verticality to it too. I think theres an incredibly interesting game they could make if they put their mind to it. And they could do it without being a shameless ripoff
I think supers can stay, but only if they find a way to make the basic attacks and specials more useful than just building up the super meter.
The stages IN CONCEPT were amazing in PS: All-Stars, but in the long run a lot of them had nothing going on.
Characters are a bigger problem, honestly.
Crash: From what we know, Crash Bandicoot is stuck in a weird legal hellscape between Sony and Activision where one company owns the first few games but the other owns the IP and characters.
Spyro: I dunno about this one, honestly. It would be great, and he'd be a perfect addition, for sure. But the problem again lies with Activision themselves, and also the fact that the Classic Spyro is basically dead and replaced with the one in the Skylanders universe (That hasn't shown up in two games, actually..)
A lot of the character selection in the first game was questionable to say the least both in terms of Sony characters (Fat Princess might have been the most unappealing character both in terms of gameplay style and how recognizable she was, also did we really need two Coles? Or a character from Starhawk?) and Third Party characters (Totally fine with Raiden and even Dante, but Isaac Clarke and Big Daddy felt less like iconic PS characters and more like iconic characters and designs from that generation of consoles as a whole.)
There are several franchises I'd love to see represented, honestly. Bring back Kat from Gravity Rush, Make a level (or make a character) from War of the Monsters, have someone show up from the Final Fantasy universe (Realistically? It'd probably be Noctis), and bring in some of the cut DLC content that never made it such as Abe from the Oddworld series and Dart from Legend of Dragoon.