With 4 engines you shouldn't. . . . . but, when you see the performance achieved with all 4 turning (due perhaps to some "flexibility" in the load-sheet) in some cases perhaps there is a case for considering the options.
Any twin /4 eng aircraft is "expected" if operated within limits to climb (well, perhaps not if you include Piper Apache/Twin Comm etc), but it wasn't so many years ago that a HS748 was put down ahead in a field after take-off from STN. If I remember there was no criticism of the PIC which was an eye opener indeed.
A bit sad you should have to consider this drastic action, but, aircraft perf deterioration with age, and aforementioned laissez faire in respect to loading may make it a necessity.
Having said that, watching early A340 normal 4 eng climbs used to leave me wondering how well it would manage on 3 without descending terrain/curvature of the earth on its side.