Wings in size between one and the other?
Of course, Willi is on all early constructions (109,110,210,410...) put the coolers on the wing, so I don't see that it would be different, but ... where is room for additional fuel - if it does go in the wing's roots, then the wheels and radiators have to be moved to the outside, so there is a problem for the MG FF (witch can't go to fuselage) , besides the biggest problem is the MG FF (drums with 60 grenades

that that second guy replaced in 110 or Fw 189). So that is our biggest problem...
Both 109 and 110 started out with 'beard' coolers. Once up-engined with DB 601, and probably for thge CoG reasons, the coolers were installed in the wing behind the spar. Advantage of the beard radiator is that it is not in the wings, so there is more CoG-neutral volume to take advantage from; it also can allow for a bomb of sorts to be carried under the belly, or a drop tank.
Same can be said for the annular radiator, and the BMW 801 might be a viable option for it. Much easier to do with the fleet of 1-engined aircraft than with the fleet of 2-engined A/C; not that the 801 is a flawless fit for the 'big fat 109', but it might have it's merits for the close support role version.
Also much easier to install the 801 on the big-ish fighter, than on the 109 that required a whole new airframe to fit the 801 (yes, new fuselage, new set of wings, new fuel tank, new cockpit & canopy...).
Weapon set-up can be 4 MG FFs - use all 4 on defensive job (kill bombers), use one pair after another on the offensive job (kill fighters).
Main fuel tanks can go under the cockpit and behind the radiator, or behind the bulk of the radial engine. Sorta like the D4Y had the bomb bay designed in.
What would it actually serve? Like fighter I don't think so, but as light fighter bomber maybe.
Bf 110 was almost bomber-sized and pretty heavy, yet it produced the positive kill/loss ratio during the BoB. It should have it's merit as a fighter bomber, and it might do well with two 30mm MK 101/103cannons, unlike the Fw 190.
It won't be able to tangle with single engine fighters any better than the Bf 110 did and it may do worse.
Streamlining only goes so far and with a worse power to weight ratio meaning lower ceiling and poorer climb (and bleeding off speed in turns faster) fighter to fighter is not looking good.
As above - while not being exactly a dream fighter, Bf 110s gave a positive account in the BoB. Problem during the BoB was that they were the only escort for the bombers past the Bf 109 escort range. My scenario allows for a good number increase of the not-110 force.
Note that as offensive fighters, the
113s are already on, say, 20000 ft and with good airspeed, and with a good deal of the fuel (100-150L?) used up. Their crews had some combat experience (some longer/better than the others), and they use the 'proper' layout of the fighter force - finger 4 instead of the Vic. Second crewman can keep the 6 o'clock surprises low.
The Defiant got to 723 Liters (?) in a 250 sqft wing but only in the MK II with the Merlin XX engine. And the only thing the Defiant wing had to hold was the landing gear.
There was a reason the Bf 110 used an 1.5 wing in the root section. It makes it easy to fit the fuel tanks in
Fuselage was the best part of the aircraft to put the fuel tanks back in ww2, so I'd suggest having the tanks under the 2-men cockpit. Wings can have small tanks to bring the fuel to 600+ L once with DB 601 engines.
Bf 110 was with 18.5% think wing at the root.
Now maybe you can make 75 or 90 round drums for the cannon in 1938-39-40 but trying for 120-180 rounds is a bit of stretch.
Cutting the ammo load for the 7.9mm guns may pay dividends. 1000rpg was rather ridiculous for the 110. (and for just about everybody else that stuffed 1000rpg of small caliber ammo in a fighter, Looking at the groundhog here).
The 4 cannon set-up is probably the low limit, together with the suggested above set up (2 cannons + 4 LMGs). Yes, bigger drums - 75, let alone 90 rd - would've come in handy.
The RAF setup of 8 LMGs might also work well in 1938-40, but I'm trying to keep this in the LW vogue
You do have a lot less room for growth/upgrades. While the 110C-4 got a pair of racks for 250kg bombs it needed 601N engines to do it and while upgraded landing gear allowed for heavier loads on later versions a single DB 601 powered plane was going to have trouble lifting a 500kg bomb or many of the combinations that the 110D/E/F did.
Needing 100 planes to carry 100 500kg bombs instead of 50 twin engine planes is not a big bargain. And the later twins could often carry a pair of 250kg bombs and pair of drop tanks.
It will be far easier to start installing the new engines on the 1-engines A/C than it was for the 2-engined stuff. Be it the new versions of the existing engine line, or the brand new engines. My
113 should not just look good with the 601N in the nose, but also with the Jumo 211s past 1940 (should be far more survivable than the Ju 87, and earlier and with less problems than the Fw 190), as well as with bigger & heavier engines. Like the BMW 801 or the really big V12s - stuff where the Bf 110 never found the favor.
Not needing to send the Ju 87s when the stiff opposition is expected ought to be worth something.
The fighter-bomber
113 removes the need for the fighter bomber 109.
As for the bomb-carrying capacity, the Re.2001 (basically the same engine and a bit smaller wing than the
113) was supposed to be able to carry
a 630 kg bomb.