I think that 'Where are we now' hit the nail on the head.
Any aircraft has to be certified for a single engine failure on take off.
That means, by definition, that with all engines running a twin engined aircraft has double the minimum amount of thrust needed, whereas a four engined one might only have thirty three percent more than the minimum, so comparing an A340 with a B777 is a little unfair.
There are exceptions of course such as Mr Boeings 744, which I once watched taking off from block 79 (half way down 09R) at LHR and he was going non-stop to Tokyo, quite impressive.