Next step up is a caliber that splits the gap between .375 and .416 as precisely as can be:
.395" monometal copper and brass (240-gr, 310-gr, 330-gr and 340-gr from CEB, S&H and GSC)
.396" LBT LFN GC Hardcast Greaser 410-grainer
Yes a wildcat, one of The Big Five Three-Ninety-Fives of my development during a long period of "wild."
Factory wood. Simple re-barrel of a 9.3x74mm Ruger No. 1-S.
Simply necked-up the 9.3mm bullet to 10.03mm, same cartridge case.
240-grainers at +2800 fps (most accurate with custom CEB MTH bullet)
410-grainers at +2200 fps (not bad with my homemade bullet)
It is no slouch.
Bare rifle weighs 7 # 8 oz.
Barrel length is 26-7/8" or call it 27".
Twist is 1:12" as it is for all of my .395 wildcats.
Harry McGowen made the barrels, special request.
After he sold to Montana the orders dried up, heh-heh-heh.
But there is one other "400/395 Nitro Express 3-Inch Aboriginal" living in Colorado, done by a friend:
I could go on and and on about the "400 Purdey Light Rifle Express" of .405-caliber/230-grain soft bullet versus a supposed .400 Nitro Express by Purdey with 230-grain FMJ solid bullet.
Ha ha.
The truth was that the ".400 S. Jeffery" of 1897 which eventually became the "450/400 NE 3-Inch" was the first ever cartridge in the later named class of Nitro Express cartridges.
400-grainer at 2150 to 2200 fps.