The 747 is well capable of flying with engines working only on one side. In fact it can fly on one engine only if push comes to shove.
Many pilots have been in the uncomfortable position to have to handle such an incident, but not only on a 747. It's precision work for the flight crew; they have to adjust the trim, work with rudder, flaps, elevators, ailerons, whatever they consider as useful in the circumstance.
There has once been an incident when a BA 747 (the City of Edinburgh) suffered a flame-out of all 4 engines due to blockage by volcanic ash over Indonesia. They were literally gliding but managed to re-ignite the engines. However, they again suffered a second flame-out but recovered again engines nos. 4 and 3. At that time, they didn't even know what caused the flame-out.
In the end, they safely landed in Jakarta after finding the glideslope for ILS was inoperative and hence having to fly the localizer with the F/O monitoring the DME. They didn't make it to the airfield but had to be towed in by a tug.
To get back to your question: yes it can. However, the most crucial moments are the seconds between VR and V2 at take-off. V2 is safe to climb out. It's a pilot's nightmare to encounter an engine failure or having to shut down one in these seconds if you're a fully loaded 747. With any other airplane, you can take-off with double thrust due to the weight but it's difficult to shove 450 tons into the sky with your engines already at max thrust.
The 747 is one of the best airplanes and can endure a lot if required and operated reasonably.
Was F/O on a 747-400.