Idea 1: Non-Canon (maybe) Crossover game [???]
This could be done in the style of Accent Core Plus (more for the ability to change the rulesets used, GG vs BB). They kinda have a way to do this without actually altering either story. The Backyard (GG2) and The Boundary (BB) could easily be the same place, with the cube-thing (been a while since I played GG2) being a version of the Amateresu unit (weakened by Sol hitting it in GG2's end, or... multiple timelines, multiple units?). Thats about all Ive gotten straightened out for this one, but somehow linking Hazama and That Man trying to get to it, meeting each other, and trying to help each other defeat the 'other' versions of each games people to help them both get what they want done. With of course the people fighting their other selves for various reasons (and giving a reason for there to be a 2d fighting version of That Man).
Switch between GG (certain version?) style and BB style, affecting mostly how specials and finishing moves work, but also Cancels and Barriers.
Music (of course, rather than a 'VS Yourself' theme, there could be a 'VS Other Self' theme
That Man as a fighter
Idea 2: (4th?) Game, a Prequel? [Blazblue 0]
This could be done in the style of Guilty Gear 2, but perhaps closer to Dynasty Warriors. It would be the story of the War, with playable characters being the 6 Heroes. Dont know who the enemies would be other than the Black Beast and monsters spawned from it/its seithr. Bloodedge would not be available at the start, but after beating the game, and hearing them talk about him during the story, there could be a prequel/epilogue chapter as the final section where you're Bloodedge holding back the Beast and its minions(?)/spawn.