How much can regeneration change the Doctor (any timelord)?

Question

We know that Doctor's character is changed with every regeneration, but we don't know where is the borderline.

He eats different (sometimes very strange) things. He is in different ages and looks. Sometimes he doesn't like soldiers, sometimes he is nearly one of them. Sometimes he gets in love or is touchy-feely, sometimes he doesn't show any emotions.
But, he always is good, he likes the Earth and people on it (although people may be questionable, when comes to some traditional series like the 1st Doctor). He is always very smart, always a man, always human-like.

On the other hand, his rival Master was evil in all of his incarnations, but

not always he was a man.

as we know.

So I'm asking, what can and what cannot be changed? Especially I am curious about the good-evil issue. Is it possible that The Doctor will regenerate once and he will no longer be good? Or are there some basic things that cannot be rewritten?

Answer 1

Regeneration is semi-random, but also can be guided to a particular result.

Mels claims she's concentrating on a dress size as she regenerates into River Song. Shallow, but it's there.

Perhaps more relevant to your question, the Eight Doctor tells the Sisterhood of Karn to "Make me a warrior" when they trigger his regeneration in The Night of the Doctor.

There is other implied evidence that even unguided, the personality of the new Doctor is at least subconciously dependent on the state of the old one. Witness Ten turning into Eleven; a doctor who started to take himself too seriously towards the end of his run turned into someone a bit more manic and childish.

Bottom line, regeneration can probably change anything about the Doctor, including his core personality - but likely only if some part of him makes the choice to change that way, and even the only minor shift to happen thus far (the War Doctor) required a conscious choice.

Answer 2

Well, we certainly know that The Doctor will get - at least - darker, if not outright evil in at least one future regeneration (even The Master agrees, sort of):

Answer 3

The implication has been that well-trained Time lords can have precise control over their regeneration, as Romana did. She simply chose to regenerate, and as such, had great control, and was able to use the period of biologic flexibility to choose from a number of forms, before very precisely choosing the likeness of Princess Astra.

Stress can be a factor as well - The Doctor is almost always FORCED into regeneration. Think of it as the ejector seat in a jet plane - it gets you away from the danger of certain death, but there's no knowing where you're going to land.

The General regenerated under stress in Hell Bent, but recovered quickly, and seemingly without mental episode. It is possible that like Romana, he (she?) had that extra training to allow better control of the regeneration, but not perfect control, due to the necessity of speed..