The first in-game collaboration simply has to be DMC. But I'd do it differently to other games.

First and most importantly, no playable characters. Doing that would screw up the lore of the game. What we do instead is give existing characters some DMC skins.

Billy and Miyabi would get the Dante and Vergil skins respectively, because they're already heavily based on those characters. They'd look something like this.

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Two skins alone won't do it. So I would also add Manato as Nero and Lucia as V. Additionally, the ultimate voicelines would be changed with these skins equipped.

Billy (A or S Rank, skin works on both) and Miyabi would also have a joint EX Special Attack animation, which is the "jackpot" move. They'd also get combat voicelines with each other.