As the B767 has wing mounted podded engines, the best scenario it would seem to me would be for the burning engine to separate from the wing.
If this were a B707 (instead of a 767) the normal drill would be to accelerate to the barber pole and hope that the fire at least is reduced (perhaps extinguished)...this has been tried in the past with this particular aeroplane, and it has worked.
Recall the BOAC B707 that departed LHR long ago, the engine separated, however, the tank valve was not closed, therefore the wing continued to burn.
Follow the fire drill exactly for best results.