This is a fanciful question. 747s are allowed to take off on 3 engines for maintenance ferries (I did a couple), but a 2 engine takeoff is not a practical or legal consideration. However, my gut level feeling is that it could be done in optimal conditions, but I'm interested in what the more technically oriented people here have to say.
The aircraft for this thought experiment is a 747-400ERF, a freighter with a basic operating weight of 351,088 lbs and a max takeoff weight of 910,000 lbs. Let's say we want to take off and make a 15 minute swing about the countryside around Moses Lake, WA with its 13,500 runway, elevation 1189 feet, on a STP day with no wind. It's flat land, there are no departure or arrival path obstacles.
We want to land with no less than 15,000 lbs of fuel, and the takeoff and flying is going to take around 20,000 lbs. Thus our takeoff weight is going to be around 386,000 lbs, which is roughly 42% of the max takeoff weight.
We have half our engines inoperative, but we are significantly less than half as heavy as the max takeoff weight. To make it easy, let's say that engines 2 and 3 are operating (the inner most engines on each side).
So, what say you?