People used to play games on piston-prop airliners, feathering one outboard engine and idling the opposite one when the weight had reduced sufficiently. However, with a jet range is always going to come with height so it would be uneconomic to shut one down.
The Nimrod certainly shuts one engine down to extend loiter and a second would be taken down to idle at light weight or even shut down completely if climb were possible on 1 remaining engine, although this would be a pretty rare situation.
A Hercules will climb with 2 engines feathered at light weight. I've been there.
Most 4-engined types will have a ferry takeoff clearance to allow the aircraft to be recovered to a main operating base for rectification. This is strictly a no-pax operation of course (except for some lunatic in a 747 who diverted into Germany from somewhere in the far East with seat straps holding damaged fan blades still). It needs a certain amount of forethought but is not inherently dangerous. It has been tested on a Tristar although there was some doubt about whether the nosewheel steering had been stalled during the attempt to keep the aircraft straight.