A generic answer because no two aircraft are the same - Caveat over!
It would be very surprising to find a 2 engined jet aircraft that did not better the performance of a 3 or 4 engined equivalent.
As you say, the twin needs more total thrust for the same weight at Takeoff. Following engine failure, similar (but not the same) performance must be obtained with 1 engine instead of 2 or 3, thus, when all engines are operating (the 99.9999% NORMAL situation), the twin has a 100% thrust excess above minimum requirements, whereas the 3 engined aircraft has a 50% excess, and the 4 engined aircraft a mere 33% excess. Thus, the 2 engined aircraft is significantly over-powered in normal flight situations.
CLIMB - A very fuel-expensive phase of flight, a poorly executed climb can destroy the fuel advantages gained during an efficient cruise, even a very long cruise. Typically, Climb Thrust is at an engine speed in excess of optimum TSFC, and the shorter the time of climb the better. Climb Rate depends upon excess POWER (Thrust X TAS), thus the aircraft with the greatest excess thrust will have the shortest climb time. The 2 engined aircraft wins 'hands down'.
CRUISE - The optimum fuel consumption occurs when the aircraft is flown at the optimum airframe speed, and the engine speed is at optimum TSFC, SIMULTANEOUSLY! Optimum airframe speed, and optimum TSFC engine speed cannot be looked at separately, they must be considered together.
Consider a 4 engined heavy aircraft early in the flight. The optimum altitude for the wing may be, for example, F/L 350, but this would require engine speed in excess of optimum, so, although the aircraft may have sufficient thrust to climb to and maintain F/L 350, engine speed will be above optimum, and the aircraft limited to a level lower than the wing 'wants'. If the same aircraft was powered by 2 engines, there will be significantly more excess thrust, thus it is much more feasible to climb straight to F/L 350 where engines are at optimum TSFC. It should be noted that in most cases, it is more fuel expensive to cruise above optimum level, than to be the same altitude below optimum level (about twice the penalty in fact). So, the 2 engined aircraft wins in the cruise phase by being able to cruise at significantly higher levels for the same phase of flight.
DESCENT - The 3 and 4 engined aircraft win slightly here, and it's their only win. As the 2 engined aircraft has much more thrust, the total idle fuel flow, at terrible TSFCs, will be more. It's only a slight win for the 3 and 4 engined aircraft, as the benefits to the 2 engined aircraft during climb far outweigh the disadvantages during descent.
That's the thumb-nail sketch for a generic aircraft.
Regards,
Old Smokey