Assuming the car checks out, and the maintenance is up to date, the maximum a car can go in one sitting is a tank full of gas and as long as you can safely operate the vehicle. And as long as you are not actively abusing the car or pushing it to its limit. 

Granted, it is better for your engine and your sanity if your car is cruising on a highway as opposed to sitting in bumper to bumper traffic or city driving. 

Going too slow can potentially overheat your car, though not as common these days. And going too slow can drive you mad. In this case, maybe less.
 
Accelerating too fast too often and redlining the engine continuously can potentially overheat your car too. In this case, maybe less too. 

Generally speaking, a tank full of gas, and as long as you can safely operate the vehicle. Me personally, Even the car can handle more, I break driving up it up into 2.5-3 hours splits and/or filling up between ¼ tank and ⅓ tank or as necessary. Gives me time to also use the facilities and grub. We need fuel too. Just like our cars.