As above unless you are going to contrive a way with a savestate (finish 4 races, grab savestate) and maybe some cheats (mostly to keep placement options and maybe AI settings whilst resetting what needs resetting) before swapping the ROM over to a secondary one then yeah that is firmly in assembly territory.
As well as any track, placement, graphics and AI changes you need to do as part of that (which is likely possible if SMK is as well understood as the rest of the mario kart series, had it not been mario kart and instead been a forgotten game like Street Racer* then you would also be learning how that works). Of course being able to make good tracks is also a thing in this and Mario Kart track making is often a lot harder than many realise.
*granted I am one of the heretics that likes the megadrive version more than the SNES one.
You will want to make sure the overall cup placement mechanic does not overflow (I don't know how many points it does on the SNES one offhand) if someone wins every race, and that the game knows how to handle that as well (I can think of several ways that would work with a fixed track count and be quicker for the program than playing sorting/ordering).
If you are intending to add a bunch more tracks you will need to find a way to have enough space. For the SNES that might be a tall order, which is to say I would place reasonable money on it having to be one of those fancy new exotic cart types various flash cart and emulator authors are playing with to get enough space and definitely if you need to add some new graphics types to it all should the base ones not encompass your artistic vision.
You would then also need to get the menu to have it available and speaking to the presumably expanded ROM. Most likely I would do another screen rather than trying to cram more into the basic one but that is likely one of those 6 of one, half a dozen of the other situations.
If not handled as part of the above then also need the game's logic to add a few more iterations on the tracks done/up next queue.
Some of this might be reduced if you did some kind of mirror mode or track replay option. I don't think this will be like later versions with easy mode and hard mode versions of the same track but if there is that then you might have some fun with that too.