[RansomOttawa]

There was a subtle hint a few years ago that the Master might become a woman, when the John Simms Master died and was cremated, and a woman picks up his ring from the pyre. In "classic" Doctor Who he also had the ability to steal someone else's body. No reason he shouldn't steal a woman's.

Switching sexes is a classic supervillain ploy. In the Superman comics of the 1940s, the Ultra-Humanite transferred his mind into the body of a woman.

On top of all that, this was just a really good episode. There was one point where the Doctor remarks that there was something very obvious that he was missing. We're then shown the obvious. It was a head-slapper moment, because I'd been staring right at it, too, and never spotted it.

[Tuxedo]

In Night of the Doctor last year, the Sisterhood of Karn offered the Eight Doctor a series of potions, one choice was man or woman. So, yes it is possible. He chose Warrior by the way, and regenerated into John Hurt’s War Doctor.