Twin Engine Pilot reported while practicing rejected takeoffs; with an instructor; the brakes overheated. On the third attempted run; the brakes failed due to excessive heat in the brakes and the aircraft left the pavement. The aircraft and pilots were unharmed.

Narrative

On a training flight for my multi engine instructor add-on rating; my instructor and I have decided to practice rejected takeoff procedures. My instructor would cut one of the mixture when airspeed reaches half of the rotation speed and I would use throttle and brakes to maintain control. The airport was quiet in the early morning; so after the 1st rejected takeoff practice; with lots of runway remaining; we performed a 2nd rejected takeoff without getting back to the beginning of the runway. Seeing that there's still lots of runway remaining after the 2nd rejected takeoff; we performed a 3rd rejected takeoff; which was a big mistake because the brakes have been getting very hot after 2 back to back rejected takeoff practices. So with the much less effective brakes; we were not able to stop the airplane on the runway. We overran the runway about 10~20 feet before finally coming to a full stop on the grass. Visual inspection revealed no damage to brakes; tires or propeller; but we could see the very hot brakes smoking for more than a minute. The cause for this incident is that we were fixating on practicing the maneuver efficiently by doing consecutive practices as long as there's runway remaining. We have considered traffic (no one else was flying at the airport) and our skills (proficient); but unfortunately didn't consider that consecutive rejected takeoffs would raise the temperature on the brakes dramatically. So we misjudged the distance required to stop our 3rd rejected takeoff.