I recall an Air France 747 did a low speed abort at Bombay rw27 and cleared and stopped on the runway turn off, to sort things out. The brakes were hot (as was the oat) and they caught fire.
Two fire tenders were dispatched, and one turned over when it did a "go direct" fully tanked, over the soft grassland.
The remaining fire tender refused to approach the 747 as all four engines were still running.
The fire progressed and the 747 was destroyed.
The fire tenders were unable to communicate with the 747 crew by radio.

At Delhi a new 747 again Air France aborted on Rw26 and slightly over ran the runway,all the passengers exited uninjured by the L1 door step (about 2ft) the 747 having ploughed into the soft earth clearway. This time there was no brake fire the wheels being several feet under the earth.
I believe this 747 was a write off.

At CDG a GF L1011 had a main tyre failure on takeoff, shortly followed by its axle mate,( the double pop sound) during the abort the remaining tyres on the same side were destroyed, and the gear leg ploughed a furrow in RW27 effectively slowing and then stopping the aircraft.
The GF L1011 tyre problems were cured I recall, by useing only new tyres,slightly increasing the pressures, and monitoring these pressures to ensure the correct inflation after every landing.
Crews were instructed on straight line taxi speeds and brake application methods, and taxi speeds in turns and the degree amount of these turns allowed.

Regarding brake application on Boeings 767/757 during aborts.
The following points I recall, and hopefully they may help.
Sometimes it is forgotten that on top of the rudder pedals are brake horns, and the feet have to be lifted well up onto these horns. They are positively and agressively rotated at full force by the pilot, with the ball of his feet,during serious high speed aborts, simple toe pressure will not achieve the stopping distance.
Often also forgotten is the immediate manual follow up of the speedbrake lever after smart closure of the throttles and the ATs disconnect.

Bhing raised two good points I'd like to comment on.

First, a recommendation to stop exactly on the centreline - fully agreed. Almost always, the runways slope laterally away from the centreline at a gradient of at least 1%, which is enough to clear rain pretty quickly, and it'll do the same with fuel. If you do have a tank punctured, then fuel will definitely flow away from the fuselage. You can genuinely stand on the runway, and watch liquid flow off.

Secondly, stopping in the middle of the runway does make it easier for the fire crews. They can then drive up the runway and deploy around the aircraft.

Fire trucks are very heavy and can struggle on soft ground. They've got the power and the all-wheel drive to grind across the grass if they have to. (We've got 6 fire trucks, and I've designed plenty of roads for them). The crews often have the training to do likewise. But the grass beside the runway might be softor muddy. The true life stories are legion - about what can go wrong can go wrong can go wrong in the process. Best to keep it easy and simple.

Overrun - if fuel isn't on fire, it won't harm you unless you drink it, but it's more harmful if it's on fire or the smoke is blowing over the fuselage.

I think it boils down to the priorities in the actual situation. My gut feeling is that most crews will want to maximise the survival of pax as it tends to maximise theirs.

What a brake fire can do for you, when not extinguished soon.BRAKE FIRE!

I see the APU extinguisher did an excellent job. :D

Can I put a question to the design of landing gears and wheel brakes?

The question arises what have design engineers so far come up with to cure live threatening (simple) wheel fires. What can be done about improving cooling agents and or onboard fire fighting agents?

So it seems that brake fires only happen on hard surfaces. If you go into the overrun or off the side and bury your wheels, there's no oxygen to sustain the fire. Something else to carefully consider in the building panic if there's no fire crew doing an effective job and the smoke and flames are increasing.
And the pax get a softer landing off the slides.
Then all you have to do is sell the chief pilot on your ex tempore brilliance while he's looking at a fat bill for pulling the a/c out of the mud and major structural repairs.