It's not really an unsuccessful aircraft, but this is one that's been in my head for a while.
Introducing the P-36/Hawk 75A series in 1938 with four Browning .50 caliber MGs (two in the wings and two in the cowl) and a Supercharged 1200hp R-1820 Cyclone (or Supercharged Twin Wasp of the same output.)
It'd be a massive improvement over the initial production run, given it's heavier armament, and it'd be powerful enough to reach a top speed of at least 330mph, with much better performance at altitude (meaning it'd be able to out-maneuver both the Spitfire and Bf 109E.)
Admittedly, only having four .50s would be kinda light armament later in the war, but considering how well Hawk 75As performed in France with four to six 7.5mm guns, it'd be a hell of an improvement, and they'd be more than capable of eating anything the Luftwaffe had at the time alive (As it was, Hawk 75As scored a disproportionately high percentage of all air to air kills during the battle of France.)
If there was a better, faster-firing .50 available, with a rate of fire comparable to the ShKAS (so ~1,600 rounds/min synchronized,) I'd also want to drop the wing guns, and take advantage of the P-36's almost obscenely low rotational inertia to make the thing the ultimate dog-fighter.
A further, somewhat insane modification could be fitting a modified P-36/Hawk 75 with a Bristol Hercules VI (in it's 1,650hp supercharged glory) and an empennage modified to balance out the engine and additional torque. Again using a constant speed propeller for improved efficiency and performance, as was standard on the initial P-36/Hawk 75.