In my personal canon I like to think that a Time Lord can regenerate twelve times without any special intervention, ergo this is their "natural" life cycle. However, should he have said intervention, a guy could in theory regenerate many more times, perhaps even 507 as an upper limit. Davies is on record as saying he wrote that bit deliberately to screw with the hardcore fans (this was in fact his last writing for Who after all), but we're still stuck with it, in-joke, real joke (who would get that, anyway?) or actual fact.
We do have proof that lives can be extended. In "The Five Doctors", the Master (who by that point had already had 1-3 incarnations after his supposed final "natural" incarnation, depending on how you look at it) was offered another regeneration and a completely new life cycle by the high council. He accepted this as though it weren't a big deal. I believe that even if Time Lord society may (or may not) have a societal taboo against regenerating longer than their physiology permits, under the right circumstances it's possible without that much to-do. It wouldn't be a permanent solution (thus why I think 507 might be that upper limit), which explains why Borusa was in search of true immortality, or as he describes it in that story, "endless, perpetual regeneration".
In any case, we learn the Master was subsequently resurrected (again by the high council) to fight in the Time War, and granted a new life cycle anyway - we see that his regeneration was under intended circumstances, and the Doctor believed that the Simm incarnation could simply regenerate again to survive being shot. Arguably Rassilon himself is a product of the same process. Furthermore, the crispy and then extra-crispy Masters (some, including myself, treat them as different incarnations of the Master due to their different makeup, character portrayal, and actors playing them) were obsessed with finding a way to extend or renew their lives. It suggests to me that adding extra regenerations is certainly possible, at least if you have Gallifrey to return to and get special permission from the bosses. It may even be possible without them, but even an extraordinary intellect like the Master found it tough to do.
I like to think that the Doctor is still effectively mortal - that he believes he'll wake up in his 13th incarnation and go "Well, that's it then... Blew my last chance at being ginger", and then simply carry on with his life. We know that it's a drag watching the show with him KNOWING he'll die at some point (see all of last season, or the almost two-year stretch the Tenth Doctor knew he was going to die since Ood Sigma told him so), so I hope that the producers by that point will choose to portray him as serene and knowing that through all these centuries, and indeed in this final kick at the can, that he did the best he could with the time the universe gave him.
So, instead of going all Mastery and looking for ways to keep soldiering on regardless of the cost, he'd barely even reference it until his time came. Expecting to die, he'd bid farewell to his plucky companion, stumble into the TARDIS, and set it on a course for a black hole, or deep space, or wherever his body or the TARDIS would never be discovered. Finally collapsing, his body failing him for the last time, he would simply exhale his last and slowly, inevitably, close his eyes...
...And promptly regenerate. He'd stand up, in full ginger glory, and exclaim "Well, THAT's different..!". Cue credits, a new mystery, and a 14th Doctor never knowing if his next death would be his last.