Question Modding to allow having multiple racers on one switch for mario kart home circuit?

I can't rule it out but generally speaking adding in splitscreen modes tends to mean something like two versions of the game being rendered at once.
You get some concessions as the same map/3d world will be being used (or at least a bit -- it might not render the whole track with every action as much as just what the player sees and then kicks the rest to something else), the same music, the same game texture data and more besides, as well as maybe being able to drop the resolution a bit (if you squish it into half or quarter the screen then you get half or quarter the resolution) but it is still a fairly demanding effort when all is said and done. Or if you prefer see the various differences that stuff sees between single player and multiplayer on most older Mario Karts -- they did not tend to do it for reasons of gameplay balance.
If there is a secondary camera mode to show fun angles during the race on the same screen at once then that can make life a lot easier as you can possibly subvert that.

The better bet for this sort of thing would be taking any tracks, weapons or similar and remaking them backporting them to another version and using that instead (I would imagine there is a fair bit of shared code already).

Adding local multiplayer is usually then only done if there is a second camera to subvert, everything always happens on the same screen (and better yet if there is an AI helper you can give controls to a human for), or while not technically local as much as emulator or network only then an AI you can disable and give controls to another player running a parallel copy with all the game data from yours copied to it.

 

Without full decompilation - probably never.