I haven't done Company Law yet but surely it happens all the time that someone is an executive director of one company and a non-executive director of another? So I suppose that you are talking only about executive directorships? Even then, I can't see why one shouldn't be allowed to be an executive director of multiple companies if:
1) The companies aren't in fact in competition and there is no sensible prospect of a conflict between the two duties;
2) If the companies are in competition but one has the fully informed consent of both companies (by analogy to other cases on fiduciary duties);
3) If one is an executive director but 'in name only' because in reality one has no influence at all in one of the companies (and so again there is no sensible prospect of a conflict because one has no duties to one of the companies).
But as I say, I haven't done Company Law yet !