Since there is no option to play the king (Mario Kart), on all consoles, you might searching fopr an alternative. There are a few and more and more coming, but is this one a good one?
Typical Mario Kart Clone, but a better one.
With Beach Buggy Racing you can see that it debuts on mobile first. But if you can ignore this and are fine with not top notch grraphic you are getting one of the better clones.

There are different game modes available, including unlockable modes. Also you are able to tweak your kart over time and more things to unlock.
Multiplayer – You can race against up to 5 player, means 6 player Split-Screen gameplay.
Quick Race – Which need to be unlocke dfirst, but just as you might expect it,
Championships – Are the Cup derivate of Mario Kart
Daily Challanges – Something you see its starts on mobile.
Career – The story and main event in singleplayer; sadly not playable in Coop (like in its sequel)
For sure you can have a lot of fun playing it alone, unlocking things and more.
But we are here at Couch Coop… so yeah the multiplayer is why you would purchase it.
But you might try it for free on your mobile to see if its sth you like, upfront.
But yeah you will need 6 gamepads and maybe a big screen, so that everyone have enough screensize for itself to play it well.
A better Mario Kart clone, but you need to ignore thats a free to play mobile game, too.
Since we are not focused on mobile, we will ignore these in our plattform list.