Ascended Fanon: Streets of Rage Remake was considered the unofficial fourth game of the franchise due to its own unique innovations to the series. So much so, that it's been stated by Word of God that it was actually part of the inspiration behind Streets of Rage 4's development, and it shows in some ways within the game itself.
One of the features of Remake was the ability to control multiple iterations of a character. In April of 2020, Dotemu revealed the same feature for Streets of Rage 4, simultaneously confirming the (pixelated) return of Skate, Max, Dr. Zan and Shiva.
Similarly, the final trailers for 4 revealed a stage called Skytrain, with guardrails to dodge just like in the alternate Stage 2 of Remake's SOR2 path. Even the icons warning you of upcoming guard rails are nearly identical.
In Remake, the nameless police officer providing the heavy firepower backup is named Murphy. In the 4, one of the riot shield mooks has the same name.
Several character animations are inspired by the Remake as well, in particular Adam's, who never had a fleshed out moveset prior to it.
Bad Export for You: 3. Not necessarily because of the inflated difficulty itself, but because the lowest difficulty setting in the overseas versions, Easy, includes Easy-Mode Mockery that cuts out the last two stages of the game, while the Japanese version's equivalent difficulty level, Normal, lets you play to the very end. In other words, you're punished for playing a non-Japanese version. Also, the Japanese version's Easy difficulty, which still lets you complete the entire game and would've been the overseas versions' Easier Than Easy difficulty, is removed altogether. The story was also completely rewritten and overhauled, turning the Rakushin bombs into just generic bombs, removing the city bombing intro, and sliding in a robot duplicate plot that replaced the Syndicate's attempts to Take Over the World with the Rakushin.
Colbert Bump: The second game's soundtrack, in particular Stage 3's main theme "Dreamer", saw a brief upsurge in interest thanks to Smooth McGroove covering it.
Content Leak: One of the final trailers for 4 revealed Y Island in the Battle Mode, which was actually meant to be a secret that's exposed when progressing in the Story Mode.
The first game started its development as a spin-off of ESWAT: City Under Siege originally given the development title of DSWAT. This explains the appearance of the police car from ESWAT when using the game's special move.
Streets of Rage being made specifically for a console worked out better as far as not having to downgrade anything, as was common for arcade ports. SoR1 was all right. The second game was great; some have even called it a masterpiece. Final Fight invented the formula, but SoR2 perfected it. It has a great balance of stage space and character definition. Capcom fans may appreciate the Street Fighter II homage/ripoff in the form of "Zamza." (That's Blanka. And Vega. It's Blanka-Vega.) Their decision to go back to the smaller characters with SoR3 was a little mystifying, though. The English release was changed for the worse with the added difficulty, and it had a more experimental soundtrack widely considered to be weaker.
Executive Meddling: For the release of Streets of Rage 4 on GOG.com, the game lacks the 2-player online feature (although 4-player co-op is included). When disappointed fans asked Lizardcube about it, they replied that the decision was not theirs, but the game publisher Dotemu. They added that fans should write to Dotemu to convince them to make the feature available to them. Multiplaying was allowed later, but only between GOG Galaxy clients.
The unlockable concept art for Streets of Rage 4 shows that several returning enemies and bosses were ultimately left on the cutting room floor, including Electra, Mona & Lisa, as well as non-pixel versions of Jack and Abadede.
The same set of art for the heroes showed two different playable characters were planned before the final version gave us Cherry and Floyd. The first was what appeared to be a version of Cherry wearing rollerblades, likely as a plan to make her a Skate expy before retooling her into something more unique. The second was a young lad with Peek-a-Bangs and used Bruce Lee-esque martial arts judging by his stance, and who also had an alternate costume heavily resembling the Great Saiyaman.
Floyd was originally a much older-looking African American man with the surname Harper instead of Iraia.
Dylan was originally to look like either a Japanese Delinquent (with a schoolboy uniform), an expy of Space Dandy, or a Yakuza thug who fought with hands in their pockets. Delinquent Hair included. There were even female Yakuza enemies as well. All were scrapped and Dylan became the final concept to fit the tone of the game better.
Lizardcube toyed with the idea implementing running in the fourth game, but removed it during playtests because the game became a running fest and reduced challenge. Therefore, only Cherry can run (while Adam can dash).
Lizardcube had access to the design documents of past games. They thought of implementing the motorcycle level mentioned above. However, the amount of work, animation, sprites needed for just one level prompted them to replace the motorcycle level with a cutscene.
The fourth game had plans to use the third game's soundtrack as a part of the retro soundtrack feature, but licensing issues prevented the developers from using it.
HidekiNaganuma was planned to be one of the guest composers for the fourth game, but scheduling conflicts prevented this from happening.
Write What You Know: Estel's haircut comes from a real-life French policewoman one of the fourth game's development team members encountered years earlier.
There was a comic book based on the second game written by Mark Millar.