At the four corners spot of Isanti (SW), Kanabec (NW), Pine (NE), and Chisago (SE) counties in Minnesota, there runs a county road east/west. West of the point, it is Isanti CR-54, and east of the point it is Pine CR-101. Even though those two counties only touch at a single point, maintenance is apportioned between two counties diagonally opposite each other.
Here is the spot in Bing Maps (https://binged.it/2FDyzcE), since GSV hasn't gone down that road. Turn around to see the Pine County marker.
Are there any other roads like that, where the jurisdiction changes places diagonally across a single point?