This game has potential for more categories. Hyper and Super categories. After beating the game and collecting all the Chaos or Super emeralds you can replay the game from level 1 with all the emeralds. Since characters are faster in their super forms, it would be fun to see how optimised the runs could be.
Misc -> NG+ already exists for starting from a save with all 14 emeralds collected for Sonic.
There isn't a huge point in doing one with 7+ emeralds, as the only difference is the lack of the hyper dash for Sonic. NG+ for the other characters would probably be added over at www.speedrun.com/classic_sonic_extensions#S3K once runs are done to see if they gain traction.
As of today, any new submissions of S3K from the Steam version will no longer be allowed. This is due to a couple of factors but mostly being inhibited availability as SEGA delisted it when releasing Origins. Any existing runs will remain unaffected.
