The .338 would have a lot of merit.

Another idea.

A .416 cartridge that doesn't have the recoil of the .500/.416.

Larger range of projectiles and a lighter rifle such as can be used for the .400's would be two potential benefits.

What parent cases could be utilised?

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On filler, another subject but ... what powder would you use in a .450 No. 2 NE ?