As you are probably all aware already, the fewer engines you have, the better your fuel efficiency. That’s why the airlines are selling off their quadjet 747s and buying twinjet 777s. It's why they’ve already sold off their trijet DC-10s, L-1011s, and MD-11s and replaced them with twinjet 767s, 777s, and 787s. It's why the quadjet A340 lost out to the twinjet A330, and the quadjet 747-8 and A380 are struggling to sell while the twinjet 777 and twinjet A350 are selling like 737s. It's why the trijet MD-11 went over like a lead balloon compared to the twinjet 767, 777, and A330.
One obvious solution to the kerosene-guzzling-quadjet problem would be consolidation: replacing the two engines on each wing1 with a single, bigger engine (for instance, replacing a 747’s four JT9Ds, CF6s, RB211s, or GEnxs with a pair of GE90s, or an A340’s four CFM56s or Trent 500s with a pair of Trent 700s or GE90s).2 However, this generates the obvious problem that the wing might need to be redesigned for the different stress distribution of a twinjet, as opposed to a quadjet, design. Still, the change doesn’t have to be large. For instance, the A340’s wing is already almost identical to the A330’s; just deactivate the extra fuel tanks, chop off the bulge under the wing that was introduced to keep the airflow around the outboard engine from breaking the wing off, take away the outboard pylons, swap out the inboards for a pair of A330 engines, and you’re in business.
Yet, despite the massive efficiency advantage to be gained, there’ve been hardly any serious proposals to reengine quadjets into twinjets in this sort of way, indicating that there’re other issues that’re showstoppers for twinjetting a quadjet; what are they?
1: I’m leaving trijets (DC-10, L-1011, MD-11, etc.) out of this discussion, as converting one of those to a twin doesn’t involve any change in the number of lateral engines - just taking out the center tail engine and making the laterals somewhat bigger. Also excluded are tail-mounted quadjets (VC10, Il-62), as these use conjoined engine pods (two engines per pylon), meaning that the two engines on each side could be swapped out for one bigger engine with little or no change in the stresses on the pylon and rear fuselage.
2: This doesn’t work for the A380, since not even the GE90 is powerful enough. Sorry, A380!