Some early 'compact twins' that might've fitted the role, some better than the others; nothing very fancy:
- 'pre-Whirlwind', powered by two Kestrel engines of 745 HP, armed with 8 .303s
- Mercury-powered 'pre-Whirlwind' (+ power, but also + drag vs. Kestrel power), 2x840 HP, again 8 .303s; both versions will need ~ 200 imp gals + drop tank facility for the long range work
- a F5F-lookalike, powered by two curent R-1830 engines, 4 .50s (US fighters of the day are lightly armed,); later up-engine with V-1710s
- press on with Fw 187 as-is, switch to Cezch-built HS 12Ys once available (Spring of 1939; easier to up-engine than with the heavier DB 601As, 20-25% better power above 4 km than Jumo 210G)
- IMAM Ro.57, but with two Isotta Fraschini Asso XI engines (less drag, better power above 4km) - a 'pre-Ro.58'; have I-F make the L.121 for a bit more power
- Potez 63 series with 'meaningful' engines, talk HS 12Y or G&R 14N
Why compact? For less drag and weight, thus for better speed, range and rate of climb.
Granted, not everyone will embrace the idea of pricy 2-engined fighters to be made in many hundreds, let alone thousands...