I've just never seen proof that twins have the enormus extra amounts of power compared to quads to compensate an engine out on takeoff. This isn't to say that twins are lacking power, they obviously have enough, its just that quads have their share also.
True, while there are some very low powered twis/quads, there are also some highly powered ones:
And, going back to twins of the days of the 707 and DC-8, we see twins of equally low amounts of power:
BAC 1-11-500: 0.239
Caravelle MkVI: 0.229
Now, to show you how I see a lack of evidence, lets compare four modern large airliners. I'm not going to use the A340 in this comparison as it is on the extreme low end of power compared to other airliners.
For a totally unbiased comparison, I'll use the highest power engine choice and highest MTOW of each of the current 300-seat sized aircraft for each calculation.
A330-300: 0.291 (one engine out: 0.146)
B777-200: 0.280 (one engine out: 0.140)
MD-11: 0.295 (one engine out: 0.197)
Il-96: 0.296 (one engine out: 0.222)
As we can see, each airliner has approximately the same about of power (0.280-0.300), be it a twin, tri, or quad. With the one engine out parameters, we see that the twins are to a definate disadvantage compared with the tri and quad aircraft. If they were to have surplus power over a quad during normal operation, the normal trust/weight ratio would be much larger, and the one engine out ratios for all would be quite similar. Yet, this is not the case.
Just for comparison, I'll add in the A340-300:
A340-300: 0.227 (one engine out: 0.171)
It has much less power than all the other aircraft, yet it still has more power than the twins with an engine out. You would think that at least the A340-300 would be surpased by the "excess power of twins for engine out takeoffs," yet this is not the case either.