Mutt - 2 points.
Once airborne from a V1 cut you always have Max thrust available from the other engine should you need it. Now your mate isn't just going to whack the other thrust lever to the stops right immediately as this is likely to make the control situation worse but on the PFs instruction or after a prompt by the other guy he may well elect to ask for more thrust.
My company uses a Laptop based system to calculate the takeoff perf. for each flight using the conditions at the time and is fitted with a database of all the airfields, runways and obstacles located at the places we fly to and from. This takes all that into account and produces the optimum performance for all the said parameters. Ensuring that all legal climb gradients are met in the event of an engine failure.
However, the Fleet Office assesses each airfield and issues Emergency Turn Procedures for each runway should they require one. This procedure is an IMC procedure that will turn the aircraft away from the high ground in the event of a loss of thrust or any condition that might affect the ability of the aircraft to clear the surrounding terrain. In this case the SID is thrown out of the window! We would be calling MAYDAY and TELLING Atc what we are about to do. i.e. left turn trk 300 then inbound to WAL 084R (in the case of runways 05 at MAN)
These Emergency Turns are issued to the pilots through the Jeppessen plates (company customised) and are repeated in the Take Off performance program on the laptop.