Our performance is checked out to MSA OEI, sometimes further. At terrain constrained airfields, there will often be a multi-part procedure, the action taken dependent on where the failure occurred, e.g. (made up example)
Engine failure before 5DME XYZ climb ahead to 1200FT QNH then right track 340DEG inform ATC.
Engine failure between 5DME XYZ and WPONT continue with SID, at WPONT turn left to UVW and enter the hold.
Engine failure after WPONT if below MSA turn left to UVW and enter the hold, otherwise continue or return.
At some places, like Islamabad, our OEI options were presented out to TOC and beyond, with escape routes coming into play once over the high ground (MSAs 27,000’+).
I’m not sure how I would feel about having a known “gap” in an OEI procedure. There are some things that are so unlikely they can be happily discounted but an engine failure in the climb out? At some airfields, it would be obvious what to do but at others, it would be easy to paint yourself into a corner and only realise this when the EGPWS starts giving input.
I am distinctly unhappy with radar departures from places where we have ETs, even though ATC should be looking after terrain clearance - unfortunately they won’t have much idea of the aircraft’s actual performance with an engine out (why should they?)