It would be a fundamental change to the game, and I don't think I'd like it. But the ABA rules allow a player to remain in the game after his sixth foul with the additional penalty of an extra free throw and the ball.
From
http://www.abalive.com/rules/- When a player has committed a 6th Foul (combination of personals & a direct technical); he may continue to participate in the game as a 6th Foul Player.
- When a 6th Foul Player commits a Personal Foul, the penalty is One Free Throw (or one additional free throw) for the offended team, plus the ball for a throw-in at a designated spot, nearest the foul.
- The 6th Foul Player Rule allows the extra free throw attempt by either one of the five players of the offended team.