I have seperated him from his TARDIS, I am a pretty avid watcher of Doctor Who but I'm not entirely sure what you mean, I know he is capable of a great many things, perhaps you could give me a for instance.... just so I am prepared.
A couple come to mind (granted this is again using M&M). First and foremost, the Sonic Screwdriver. Normally I only used it as a door opener and scanning device, though in the 9th and 10th Doctor eras it became somewhat Deus Ex Machina-y in the area of problem solving (
here's a full list of it's functions through the years). Because of that I kept its use limited as to not override the players abilities (including limiting it when I played The Doctor in Tom's version of the game). Also, The Doctors telepathy. Granted I've only seen it used a handful of times but it can sometimes advance the plot further than you want to if the player abuses it just right. A way though you could limit or rein it in is to possibly throw in unexpected difficulties (e.g. Pain from the psychic "headbutts" presented in "The Lodger" episode). There are possibly a couple of other issues, but I can not think of them at the moment. When playing him, I usually presented him as a walking Hitchhikers Guide to The Galaxy.
Edit: Another thought that could be fun that I've yet to explore is a possible regeneration in-game. That could create an interesting scenario in which your PC has to come up with a completely different personality while essentially inhabiting the same character.