Platinum Games F-Zero.
You have your basic grand prix modes and characters but there's a story mode where you play as C. Falcon where levels alternate between action beat-em-up and racing segments.

Blue Falcon and other hovercars can be customized by gathering parts around the story mode and winning them in races. A challenge mode is also available for both forms of gameplay, a gauntlet similar to the Bayonetta witch trials and racing challenges as well.

Character cameos from other Platinum properties/games from Nintendo consoles, including Bayonetta in a hoverbike inspired off of the motorcycle she has in Bayo 1 and Akira from Astral Chain in a Neuron themed hovercar.

Levels in the action mode take place in various areas in the F-Zero galaxy, you'd obviously start in Mute City and progress from there. Evert few levels you'll fight a prolific character as a boss (Samurai Goroh, Pico, etc.) Black Shadow would serve as a rival throughout story.

Might add to this thread later. If I keep going I'll probably start sobbing bitter tears because none of this will probably ever happen.