WMG: Bakemonogatari

Karen is also some kind of supernatural creature, or at least partly touched by the supernatural
It's hard to otherwise explain her phenomenal physical strength - no other human character in the series exhibits anything remotely close to it without using magic or getting aid from a supernatural being. Given that her brother is a vampire and her sister is a phoenix without even knowing it, it wouldn't be all that much of a stretch.

Impossible crossovers

Okay, honestly, I only started thinking this because I noticed Takahiro Sakurai voices both, but it's not that out there, is it? It's been noted that both shows have similar formats and concepts.

The Medicine Seller is immortal, and if he is a mononoke like on Mononoke's WMG, who says he can't shapeshift? He didn't bother back in the 1920s because while his outfit was rather out of place, there were still people running around in kimono back then, so nobody made a huge deal out of it. Nowadays everybody would call him out on it, so he traded in the ridiculous kimono for a ridiculous Aloha shirt. As for whatever happened to his sword...perhaps it became corrupt some way or another and became Heart-under-blade/Shinobu, who has occasional access to an absurdly sharp sword.

Shinobu is/was a one of the 27 Dead Apostles
Well, she was a vampire. And in the first episode, during the Fake-Out Opening I swear, there was a priest and a few other things. I haven't read the light novel, but maybe an attempt to seal her by a burial agent? As for Araragi, his case was like Satsuki, where he was one of the 1 in 10,000 able to become a vampire and also able to skip the first two steps.
  • Type-Moon vampirism is permanent.
  • Indeed it is, but nothing is impossible for the Medicine Seller (see above).

Oshino somehow knows Yuuko.
For one, they both deal with the supernatural. Two, Yuuko seems like his Distaff Counterpart. Three, they both have a Watanuki-like figure (i.ie, an adorkable teenage boy whom they love to tease. Lastly, they both disappear at some point, leaving their little teenage boys alone to fend for themselves... sort of. What this troper wonders most is why he hasn't written a crossover of xxxHOLiC and Bakemonogatari.

Apparitions are the forms that mushi take in the modern world.
Following WWII and the surge of Western values into Japan, people began to no longer accept the existence of mushi. As a result, they turned into becoming things far more supernatural than animalistic in nature. This means that Oshino is one of the few mushishi still doing that job; as we can see, it's probably not very profitable so few do the job anymore. This is not even taking into account Koyomi's similar appearance and personality to Ginko.
"You can't hate an animal for doing what nature made it to do."
"It's wrong to pin blame on an apparition, because they simply are what they are. That's all there is to it."
-Koyomi Araragi