From this DWAITAS thread about a game where the players are all Time Lords:
In rules terms, this shouldn't be a problem. The characters might feel a bit samey, as they all have much the same superhuman abilities (regeneration, boosted Ingenuity) but different opinions, styles and gadgets should counter this.
An alternative would be to have all the characters be remarkable in different ways - so there's a Time Lord, an unkillable man from the future, a Nestene duplicate with a human soul, a Victorian Silurian ninja detective...
One thing you could lose in character terms is the sense of wonder and surprise about travelling in time and space. Time Lords (even less experienced ones) can be blasé about meeting alien races, seeing the birth and death of stars and planets and the like. It could feel very different from regular Doctor Who.