Yes I suppose. The Time Lords were able to give the Master a new "set" of regenerations in a classic episode (sorry I can't remember which) and the Doctor said in SJA that he can regenerate 507 times. So from what I gather, biologicaly, 507. Gallifrey law, 13 :) hope this helps!

I'm pretty sure the 507 thing was an Easter egg to fans. 5+0+7 = 12, which is his number of regenerations.

Well, it's actually a psychological limit, as in Time Lord minds can break down after twelve regenerations, or at least so the Virgin New Adventures claim. The episode you are thinking of is "The Five Doctors", in which the Master, trapped inside a mortal body he stole off of Nyssa's father, is offered a new set of regenerations if he completes a task in the Death Zone, but he doesn't actually complete that task, and the fact that he later goes to the extent of stealing more bodies to escape from the Cheetah Virus implies he didn't get those regenerations in the end.

So far, we don't really know where the limit of 12 regenerations (13 incarnations) comes from. The fact that the Master could be offered a new cycle and (very importantly) that he didn't express any doubt that a new cycle was possible, indicates it's not a hard-and-fast limit. If, as referred to above, it were a psychological limit, the chances are that it would be a bit variable: some individuals would break down after fewer than 12 regenerations, others would manage to hold on for a few more than that. The offer to the Master of a complete new cycle of 12 regenerations argues against it being a psychological limit in exactly the same way it argues against a physical limit. The Time Lords didn't offer him the chance to risk further regenerations; they flatly offered him 12 more and he was sure they were able to deliver on the offer (though he might have been suspicious about whether on not they really would do so). Of course, the limit of 12 might have been imposed because that was as many as would be safe and the psychological dangers wouldn't arise until after that number. Even so, if the Master had thought it possible for him to regenerate more than 12 times without the help of the High Council, he'd have tried it.

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