Thanks for all the replies, especially tdracer, and wiggy.
While we all know that the airplane can reject at take off weights so obviously it can land again, this is probably not something we want to do unless in a land immediately situation, Tires melted for sure, probably the brakes finished, and maybe even an evacuation due to a brake fire underneath all the fuel. I have seen some pretty dramatic videos of near V1 reject flight testing.
My own airline had a few cases of airplanes returning heavy after flap issues. The performance charts said it could be done, and it could (and was). The last one required the mechanics to cut the melted brakes off the axles. We were then issued non mandatory "guidance" that suggested dumping to max landing weight (or more if required) any time we were dealing with an aircraft problem. Obviously this requires flying around in circles for half an hour in the manner FlightDetent alluded to. And obviously you wouldn't do this if there was any doubt as to the integrity of the other engine or if something was on fire, but the risk of an apparently healthy ETOPS certified engine failing in a particular 30 minute period should be extremely remote. Our guidance will try and have us avoid dumping unnecessary fuel and land overweight if there is nothing wrong with the airplane and runway length permits.
I guess I can see the logic with this. An overweight landing requires a gentle(ish) touchdown in the touchdown zone to take advantage of all the available runway. An engine out, flap, or flight control issue introduces potential handling complications that could work against the objectives of the overweight landing. Why combine the two if you don't have to?
Anyway, we saw this in a sim scenario and I just wondered what the collective wisdom was. On the sim scenario in question, the matter was resolved by a pop up notam that reduced the useable runway length and required dumping fuel.
Cheers Cropduster.