There are plenty of examples, but if you want a classic then perhaps the Supermarine Type 300 fits the bill. It began as a cleaned-up Type 224 but, as first presented to the Air Ministry, retained the Rolls-Royce engine with evaporative steam cooling and a straight, tapered wing with room for around four machine guns.
While it was still on the drawing-board the PV12 engine moved to glycol cooling and "Merlin" monicker, the Ministry requirement to eight guns and the wing to thinner profile and elliptical planform. Yeah, the Spitfire.
That famous D-section main wing box is in fact the legacy of the evaporative cooling system.
Here's another almost as classic. When Convair first flew the prototype delta-winged jet interceptor the YF-102, it sucked. It handled like a pig on the approach and couldn't even go supersonic in level flight. Two new discoveries at that moment included area-ruling and conical leading-edge camber. Both were applied in somewhat ad hoc and hurried fashion to the YF-102A and it made Mach 1.25 in level flight, while also being a lot tamer on the landing flight path. Time for a breather and a proper job with 50% more thrust to boot, and the F-102B, renamed as the F-106A, happily hit M 2.3.