What clean-up profile is used with MCT or CLB power? Every clean out profile I've seen, on multiple jets, uses takeoff power. If the normal profile doesn't work runway specific engine out profiles are developed.
Our airline had a famous (infamous) example where the crew tried to clean up using CLB power. Descending turn from base to downwind just a couple of knots above stick shaker. They were unaware of the proximity to stick shaker because the minimum speed tape information isn't displayed on Boeing's until the first flap retraction. No flap retraction = no minimum speed tape information. This incident became a company wide, and FAA (?), required training event - engine failure after thrust reduction altitude but before flap retraction. At light weights the plane might be able to accelerate to clean up speed with MCT. At heavy (normal) takeoff weights they won't. The engine failure SOP changed - there is no clean up profile with CLB/MCT. In the event of a takeoff engine failure after thrust reduction but before cleanup - return to takeoff power or TOGA for clean up.
This event links to another training event for arrivals - non precision approaches, single engine, at heavy weights. Scenario was max takeoff weight with uncontrolled fire. That leads to an immediate return using a non precision approach. The standard SOP is configured at the final approach fix. The reality is the plane can't maintain level flight, configured, with an engine out at heavy takeoff weights. At a light weight it might. At what weight does that become possible? That's a decision that needs some Clint Eastwood advice "do you feel luck?" Or you can adjust the single engine non-precision SOP to "no gear down unless you're going down." Step down level offs can literally be a killer.