See the Fw 187, which was flown as a single-seater and two-seater, the latter in competition to the Bf 110
Except it really wasn't in competition with the Bf 110.
Focke Wulf may have wanted it to be but the Luftwaffe didn't see it that way.
The Fw 187 was later in timing than the Bf 110 which meant a few advantages, like being tailored for certain jobs. Which helped with better performance.
However it also means that the Bf 110 production would have had to be shut down and Fw 187 production started up. Granted it took a while for the 110 production to really get going but that was also due to a shortage of DB 601 engines so they just trickling out Jumo powered 110s.
Part of the 110s problem with performance was it was really a 3 seat aircraft. Most of the time it was flown with a 2 man crew but the cockpit was huge, which turned out to be a very handy as a night fighter when it came to fitting in the radar equipment and/or the vertical guns. It was also handy fitting big recon cameras into the cockpit. The wing size came in handy when carrying drop tanks and bomb loads. However it also means you don't get much change in performance from cutting off most of the canopy and plating over the hole. You don't get a sports car by cutting the roof off a station wagon (estate car).
The 187 was tiny in the cockpit area. The 187 had very good handling with the Jumo engines, Shifting to DB 601s is going to get you into P-38 land as far as performance goes. However it is also going to get you into P-38 land as far as wing loading and roll response goes.
187 as built (Jumo engines) carried 1/2 the 7.9mm ammo and 1/3 the 20mm cannon ammo that the db 601 Bf110 did.
P-38s carried or had room for (probably shouldn't have) a crap ton of ammo and heavy guns.
The 187, needed the next generation of guns (MG 131 and MG 151/20) to really become effective.
Let's also remember that the Me 210 first flew in Sept 2nd 1939. Granted it was plagued with problems but that is closer to what a DB 601 powered Fw 187 was competing against than the Bf 110.
The 110 was too big to be converted to a single seater. And a single seater with two DB 601 engines, while faster than the 110 still would not have been able to turn with, roll with British single engine planes.