[Kiwami]

What a fantastic idea. I'm a sucker for thematic matches, so the following come to mind:

Drive and Accel. Granted, they kind of did this themselves already in "Kamen Rider Drive Saga: Kamen Rider Chaser", but it's too good of a combo to not feature in a dedicated story. I'm imagining Roidmudes getting their hands on Gaia Memories forcing both jurisdictions to work together, which of course isn't going as smoothly as one would hope. We already kind of have an understanding of how these characters would interact because of the official crossover so I don't really need to explain it further.

Ex-Aid and Birth. Mostly because Ex-Aid had all kind of doctors, but none of them are like Akira Date: A doctor who works in crisis hotspots and tries to make the world a better place in the direst of places. Seeing him work off of the cast and interact with Emu, Hiiro and Taiga would be interesting. Honestly I don’t have a particularly good idea how it would happen, knowing Date he might just pass through town when a particularly nasty Bugster infection takes place and he offers his help. For cash money, of course.

Kiva and Specter. Ghost is icky and I don't like it, but giving Kiva another "supernatural" Rider to work with could be fun. And I prefer this combination over something from Wizard simply because the characters wouldn’t mix as well. Wataru on the other hand would clash so well with Makoto. Wataru is soft, undecided and often lost in the world, Makoto sternly moves forward with a single goal in mind. They would annoy each other to no end and I'm there for it. Plus, it would all be worth it once the vampire and the ghost kick some Fangire-butt together. As an enemy I imagine a special Nightmarish Fangire who can travel between worlds and has knowledge of the Gamma plane of existence.

And now for something completely random which I came up with just because:

Build and Baron. Simply because Sento's ideals of "Love and peace" and Kaito's "Power through transcending compassion" would make them bitter enemies. It's not much of a team-up but rather a confrontation so their story would actually be more about convincing the other than anything else. Also, Banana & Knight Fullbottles for more crazy combos.