If they do go beyond the 12 regeneration limit, best not to explain it. Just leave it as a mystery of the universe. After all any attempt to explain it is going to annoy some part of the fan base (true so will not explaining it)
But in the case of River, she got her regeneratgions in part because she was concieved whilst traveling through the vortex. Who knows perhaps all those centuries of travelling through the vortex have had an impact on the Doctor. Whilst most time lords stayed at home.
I too have thought about him simply getting more Regeneration juice from al his travels in the Vortex. IIRC, In the Gallifrey Adventures (Or perhaps Zagreus or Neverland) Audioplays, they specifically attribute the Regenerations long life of the Time Lords evolving precisely from travels in the Time Vortex
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?