The "Rim-to-Rim-to-Rim" (R2R2R) is a world-class route, staring on the South Rim of the Grand Canyon, running 5,000′ down to the Colorado River, across a bridge, then 6,000” up to the North Rim. Then back again. Records have been known for decades for doing this on the South and North Kaibab Trails, crossing the river on the bridge near Phantom Ranch. These are recorded here.
The South and North Bass Trails also allow passage from the South Rim to the North Rim. While the elevation/distance profile is very similar, these trails are small and scrappy compared to the "Corridor" Kaibab Trails. Plus, there's no bridge so you have to swim across the river. Buzz Burrell named this the "R2R2R-alt".