Eighth Doctor Adventures/WMG

When Fitz became an Artificial Human, the TARDIS interfered with his personality to make him a more ideal companion.
There's a fairly obvious shift in his personality following Interference. Prior to Interference, he seems much less trusting of the Doctor and much more likely to bunk off at the first opportunity. However, he eventually becomes much more heroic and almost scarily devoted to the Doctor. He knows for a fact that the TARDIS has changed the way his brain works: his dreams are overly normal, he can generate anagrams with his brain, and his thoughts have a "deeper structural underpinning" that computers like (even if they're the same slightly Cloudcuckoolander-like thoughts he's always had). And there is precedent for companions being mucked around with like that in the EDAs: Sam was changed completely from a troubled, cynical drug abuser with dark hair to an earnest, blond Soapbox Sadie who eventually comes to the belief the Doctor "never never never does anything wrong" due to contact with his post-regenerative biodata. Considering the difference between Fitz's personality at the start and end of the series and how much the Doctor ends up relying on him, it does seem rather as though the TARDIS thought this all out pretty well.

Trix isn't human.
Well, she says so, although Trix says a lot of things. "‘So you tell me – how long have you been in the TARDIS?’

[Trix:] ‘Months. At least, I think it’s months. It might be years. Centuries even. Do I look a hundred and fifty to you?’

[...]

‘In my reality, humans don’t exist at all.’

Jack stared. ‘You mean you’re not a human being?’

A slight smile. ‘You asked why I was practising. Now you know.’

‘But you look human.’ And you’re a show-off. But he didn’t say that bit. ‘I don’t think you’re telling the truth.’

‘It’s called plastic surgery, Jack. And a little bit of jaw reduction.’ She looked away. ‘You see, there’s a reason why humans went extinct in my reality. We ate them.’

Jack had to laugh. ‘Now I really don’t believe you.’

But she just stared at him, with those catlike eyes, and the laughing dried up in his throat."

She's almost certainly lying at least in part, but her "catlike eyes" are mentioned so often that there's a distinct whiff of Ambiguously Human about her. Also, as a Master of Disguise, she certainly has the skills to cover it up if she's an alien. You also have to wonder why it would occur to her to say such a thing if she is human. And considering how heavily populated the Whoniverse is with Human Aliens, why not?

Fitz's stomach is literally a black hole, and via wormhole it transmits most of the food he eats to Sabbath.
Fitz is always eating. Sabbath is seen eating pretty much a grand total of once. Looking at them, you'd expect it to be a bit more the other way around. We could be reasonable and assume Fitz has a speedy metabolism and Sabbath generally takes his meals in private, but where's the fun in that? This might also explain why Sabbath is so unreasonably resentful of Fitz, who does very little to earn it; he knows what's going on and it gets on his nerves that Fitz eats like there's no tomorrow.

Fitz is a Time Lord.
He's obviously married to the Doctor, and maybe you can be a Time Lord by marriage or just by spending too much time around one. Alternately, see the first WMG. Perhaps the TARDIS thought that the ideal companion for the Doctor would be another Time Lord, who would never die and therefore would never have to leave him. Also, he somehow manages to figure out when it's his birthday, even though everyone else who travels in the TARDIS, at least everyone else who's human, completely loses track of time. And he's on the right track for getting the whole Doctorish thing down well enough, which is generally used in This Wiki as a criteria for Time Lord-ness.

The Ninth Doctor's leather jacket originally belonged to Fitz.
Fitz often wears a leather jacket, which he's had to replace several times because things happen to it. For example, giving it to the Doctor happened to it, in The Ancestor Cell, when the Doctor is suffering from a severe Heroic BSOD and is about to be left to Walk the Earth for a hundred years. It would be more heartwarming if the Doctor were ever seen in it again... Anyway, it's possible that he somehow hung onto it, and starts up wearing it again after he regenerates, perhaps as a memento of Fitz after Fitz leaves him or dies. Alternately, Fitz just feels protective of the Doctor at some point during the Time War and gives him his current jacket, which, again, the Doctor hangs on to.

Sabbath is intended to be some kind of Übermensch
Well, maybe. This may be the reason Lawrence Miles got kind of mad about his Villain Decay into a more overtly villainous but overall less threatening character. See, he's this antiauthoritarian sort of guy, who in the 18th century shaves off his hair because he just does not have the time for hair, and takes a mute native girl to social functions because it amuses him. He only deals with social conventions if it suits him to do so. It's not that he has No Social Skills, but he sometimes acts like it because at the time, social skills are not what's useful. His personality makes complete 180s depending on the situation: he acts Wicked Cultured or like a Boisterous Bruiser, or just a completely different person, all for the sake of being a Manipulative Bastard. Because of this, he's very charismatic. (His commanding voice helps, too.) His relationship with the Doctor is rather volatile just based on whether or not the Doctor is useful to him alive or dead. Even his Morality Pets are primarily kept around because they can kick your ass. And he's prone to thinking Murder Is the Best Solution. So, he's pretty much The Spock, but, interestingly, unlike the typical Spock, isn't from a culture where massively prioritizing logic is normal; he just got this way on his own.

He's also planning to completely alter the basic functions of reality: he wants to completely alter the whole entire multiverse, so that it's only one universe and doesn't branch off into other universes every time a decision is made, with a side of planting human DNA at the Big Bang so that the universe will be dominated by humans (because Humanity Is Superior). Also, as far as the aspect of Speculative Fiction Übermenschen tending to have some kind of superpowers, he is inexplicably Made of Iron and in one book develops the temporary but impressive ability to teleport through time and space.

Another thing: the basic point of his character was originally to replace the Doctor, and when he first appeared the Doctor was The Last of His Kind and a dying amnesiac, suggesting some sort of allegorical God Is Dead... thing. And, in accordance with Nietszche's statement that not only is God dead, but "we have killed him", Sabbath is supposed to be killing the Doctor, although for a few reasons, he keeps saving his life instead (which he decides to rub the Doctor's nose in). The only problem is that his whole quest is kind of other people's ideas, even though he seems quite personally invested in it. Is he a subversion of the Übermensch... or is he just using his bosses, too? It's unclear. Also, he keeps screwing up, which isn't terribly Übermenschlike, but oh, well. Anyway, he does hit all the major points: The Doctor is a bit the same way, though, when it's put that way, but doesn't really have any particular guiding plan other than wanting everyone to be happy and safe, and is more of The Messiah.
 * Big ideas
 * Complete disdain for social conventions
 * Highly charismatic


 * Erm, the reason Miles got mad seems to be more along the lines of Sabbath being intended as more of a Rival Hero Antagonist rather than an outright villain, not from having supposed to have been any sort of Ubermensch. Doesn't disqualify Sabbath for the position, but just saying.
 * Alternatively, Miles just likes getting mad. He's a bit like that.