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Let's make things clear, to start with… From the get-go, nobody is saying 'ret-con.' Outside of some truly dire situations, the problems should be addressed rather than wiped away. The changes given here will not change how V unfolded but, rather, give some potential new hope for it.
Soulcalibur V was a big disappointment and the reasons are numerous. From the loss of series mainstays and lack of explanation for why they were removed, to an underwhelming story mode and a weak online mode, it's not really a surprise that it failed. However, that doesn't mean it can't be redeemed, either. Here are some simple suggestions:
1.) Bring Back Old Characters
Unquestionably, the most obvious option is to bring back the old cast - it seems like a no-brainer. One of the problems V had was that many of its characters simply disappeared. Talim, for example, was just gone. No reason given. She was just not there. Xianghua suddenly ditched Kilik and had married a general with several children. Cassandra was nowhere to be found, yet Sophitia was the new physical form of Soulcalibur? Bringing back the old characters as 100% playable is not a requirement. In fact, it could be argued to be the exact opposite, as some of them are ageing and others, such as Rock, simply may not hold a place anymore. However, that doesn't mean they should just vanish completely, either. There is no reason Taki cannot be outright training Natsu instead of simply shoving it into back-story. Even if Taki can't be played, at least letting the player have Natsu fight against her as a 'graduation' of some sort would be more satisfying than simply letting her vanish.
2.) Focus On the In-Between
One of the bigger issues was that between IV and V, there was a huge time gap. This, itself, is not a problem. However, it leaves a huge gap in which things can actually be explored in the interpersonal relationships. How does Patroklos see Setsuka and why did he pick her to be his mentor as opposed to learning how to use his mother/aunt's weapons? How did Tira watch over Phyrrha as she grew? Why did Xianghua and Kilik break up? While not all of these questions need answering, they would provide a far more defined focus than simply another scramble for the swords. Speaking of which…
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3.) Explain How Soulcalibur Turned from 'Good' to 'Order'
In V, the title weapon, formally the basically-unquestioned 'good' of the series, suddenly changed. No longer was it the good weapon that the characters on the side of good sought to beat Soul Edge but, rather, an antagonistic force. There are potentially many ways to explain how this happened, such as something corrupting it from the inside out; however, simply turning it into an antagonist is a bad idea. It insults all the characters, even guest characters like Link, who fought for it, since it changes the mechanics between the two weapons. Now Link didn't fight to stop evil but, instead, to help out something that may have been just as villainous as Ganondorf, just with a woman's body. Zelda will likely condemn him to sleeping with the cuckoo's now…
It's not that this transformation can't happen without depriving the good characters of what they fought for rather it's that it needs a reason for such a shift to happen. Seeing such a shift would, likely, make for a far more interesting story than just going 'lol I R evuls now.'
4.) Don't Skimp on the Single-Player
Soulcalibur II had the weapon-master mode, III had the whole campaign, IV at least let you play as each character, but V ditched that… and it shows. A viable single-player campaign is actually quite important as it gives a reason to play the game outside of either fighting friends or getting ready to fight friends. It doesn't have to be something overwhelmingly epic but if you are losing the single-player fight to, literally, every other fighter out there, simply because you have locked it to one character, there is a problem. It would be better to look back and find a way to improve what II or III did than to simply avoid it completely. One very potential idea is to make something akin to Fire Emblem, except with battles between characters resolved via fights instead of stat comparison.
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5.) Offer Something Unique for the Online
Anyone can do a Quick Match. It's not hard at all, so long as there are stable servers. What you need is something to actually stand out to draw people in to play. One idea would be to make it so that each player can gain access to a small plot of land that they can improve, fight bandits or other players to gain land, and then have to defend it. Maybe they can opt to join an army... Maybe they can go battle it out in an arena... Maybe they can try to hunt for a weapon… While it could potentially go all the way to full-on MMO status, the basic premise is simple. Give gamers a reason to want to play online, especially for those that are not mega-player.
6.) No DLC
No. Just no. At the least don't put series mainstays behind it and instead keep it confined to guest characters. If there must be DLC, then make it costumes, alternate skins, and the like. Locking someone like Siegfried behind a pay-wall will just drive people away.
7.) Make Amy as Viola
Between their designs, likely age difference (especially if she's dabbling in magic), voice actors, Amy's mysterious disappearance and Viola's convenient amnesia, and other things… it would be much worse to find out Viola is not Amy than that she actually is. Making Viola Amy actually opens up a bunch of plot possibilities, such as dealing with her falling out with Raphael (maybe she realised where he was going and decided she wasn't going to follow that path) and how she learned magic (maybe Ivy?). Dancing around like this in regards to her identity is just annoying.
8.) Get Rid of Guarding Penalties
In IV and V there were penalties if a player ended up guarding too much. While this sounded good in theory, it ended up resulting in situations where one player was forced on the defensive against a character with high offensive momentum and couldn't break out, watching as their gauge slowly depleted for a terrible ending. This should not happen. It would be much better to make it so that guarding isn't always the best choice (such as blows strong enough to knock a character off-balance and open to attacks) and make it so that someone can gain an edge too easily.
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9.) Don't Limit the Guest Characters
Guest characters are awesome so long as they are not overused. A lot of people bought IV simply because Vader and Yoda were in it. Between Hehatchi, Link, several unique designs for III, Vader, Yoda, and Starkiller, Lloyd, and Ezio, almost all of the guest characters have been hits… except for Spawn. That may be more about being on the Xbox, though, and up against a Zelda character and one from Tekken, however. Some good ideas would be whichever Tales character is current, Neptune from Hyperdimension Neptunia], Ike/Marth/Corrin/Lucina from Fire Emblem, or even something as out-there as whatever they decide to call the main character for The Elder Scrolls VI. It doesn't really matter. It's more fun to watch Sailor Moon beat up Astaroth before switching to Ruby Rose from RWBY to fight Zasalamel in a scythe-off than to have the developer go 'No! Because… reasons!' Obviously, the guest characters shouldn't usurp the main cast, but pig-headed denial is potentially far more frustrating than letting a high-demand or interesting character in.
10.) Remember That Variety is the Spice of Life
Having a bunch of clones, characters who utilise random weapon styles of other characters, or characters who just fight too close to another is just… wrong. Not everyone needs to wield a different weapon, like Hilde, or be distinctly different, like Viola, but seeing a bunch of sword characters, cutting some of the unique ones, and then inserting clones and weapon-master style characters, is just not the way to go.