Each upgrade type has 9 possible upgrades in 3 stages. In total you can have 24 Upgrades on your Car with a possible 27 available.

To upgrade your car, select the car from your garage and click upgrade. There are 3 upgrade types: Engine, Weight, Chassis. After the first 3 upgrades for each upgrade type (Stage 1), you need to select three cars you no longer want to use to 'fuse' into your car to upgrade to Stage 2, and the same for Stage 3.

As you reach each upgrade stage, you will be required to 'Fuse' - see 'How do I fuse' for more info. 

It's possible to have two of the same cars with different max attributes, for example you could specialise in Engine with Stage 3 maxed for Top Speed, and on the other car specialise in Chassis for Grip.