The company that I work for has a number of engine out procedures that require that have airspeed restrictions during clean up in the 3rd segment. To do this the flight mode has to change from take-off to speed select and level change resulting in the aircraft climbing above the engine out acceleration altitude until the point where the speed restriction no longer applies and then accelerating again to finish the clean up.
This is very vague. It will be clear if you give an actual example. What is the speed restriction F, S or GD? and which aircraft is this?