I've done stuff like this before, a couple of times. Only once solo, though... drove from central PA to Madison, WI in 15+ hours, starting at 11pm (I tend to be more alert driving at night than during the day.)
I was doing fine through most of the night, with frequent calls to people to keep me awake (not to mention the MASSIVE thunder/rainstorm that pounded my car for half of the ride)... but right around dawn, I started to crash. I had to pull over at a rest stop and nap for 1/2 hour or so before starting again, and was fine after that and a cup of coffee.
I will say that as far as staying alert, I've found that music choices influence me a great deal. I HAVE to play music that I know all the words to and can sing along with... that's what keeps my brain engaged and awake. If I am listening to unfamiliar radio music, or something really slow/depressing (e.g. Radiohead is a NO NO), I get sleepy immediately. So I recommend getting a lot of music that you can engage with somehow, and not be passive with... otherwise it will put you to sleep. Just my advice.