as far as i know the operator is responsible to create an engine-out proc. so different companies might have different climb-outs for a given runway.
with us it's mostly straight, min flap 800AAL, but the take-off-performance software on the laptop always tells us clearly what to do.
terrain situation might lead to turning procedures and the engine-out routing is available as FMS-routing with has to be EXECuted on the box after liftoff.