Was it ever considered to optimise a jet to normally operate with one engine shut off? As I understand it, the current trend to reduce all commercial aircraft to no more than two turbofans has long-relevant reasons – the more engines, the higher the fuel consumption – and earlier jets mostly had to come with more to ensure reliability.
Now, the naïve solution to design an aircraft with 3 or 4 engines but needing only two has obvious economic flaws and a normally mounted engine introduces so much drag that it's certainly always better to run it than not. However it is not unheard that existing aircraft designs were upgraded with better engines (particularly for economic reasons: stern look at 737MAX). I'm thinking particularly of trijets here: the 727 for instance did have its outboard engines upgraded to higher-bypass ones in its career. I could well imagine that they thought about whether the center engine could be made obsolete altogether – just make the new engines 50% more powerful each, and thus degrade the center one to a mere emergency backup. (And do something aerodynamic about the S-duct so it wouldn't be too detrimental for drag anymore.)
Was any such redesign seriously pursued by one of the major manufacturers?
I can think of one example: the Hawker Siddeley Trident 3B.
This had a fourth, small engine buried in the tail, which was only used during takeoff. They did this because it was cheaper than redesigning the aircraft for different engines.

Since the Spey 512 was the last of the Spey line, extra thrust would be difficult to obtain. Instead of attempting to replace the three engines with a completely different type, which would have been difficult with one engine buried in the tail, Hawker Siddeley's engineers decided to add a fourth engine in the tail, the tiny Rolls-Royce RB162 turbojet, fed from its own intake behind a pair of movable doors. The engine added 15% more thrust for takeoff, while adding only 5% more weight, and it would only be used when needed. BEA accepted this design as the Trident 3B, and ordered 26.