You might have noticed that in recent history, any aircraft that needed more than two engines went straight to four.
I think the reason for this can be pretty easily seen- the convenience of pod-mounted engines.
They allow an uninterrupted Fuselage design, have no problems with intake, are very easy to maintain and remove, and actually have a structural advantage acting as a counter-weight to the wing attachment point.
What you are proposing has all the inherent problems of a tri-jet- mounting an engine that needs air coming into the FRONT at the BACK of the aircraft, with the additional hurdle of needing TWO of them (your "emergency" engine is still going to have to intake air!!)
The pure economics of single v twin would be as persuasive as twin v quad- but the engineering would, I think, make it a non-starter.
As an aside, Douglas were proposing a twin variant of the DC 10, but figured the restrictions on twins would make it non-viable. Enter the B757/767 and ETOPS.... We'd probably still have a "Big Three" if they had gone ahead with it!