I may be overlooking something that is already well known, but refuse to believe that no one has necked a .375H&H case down to .338cal.

If so what is it called?

Neck it down and blow it out and you have a .340 Weatherby. Sean

how about if we maintain a conventional shoulder?

I believe that would be very close to the original 334 OKH, from back in the 30's. Elmer Keith and friends necked down 375 brass (both full length and shortened versions) and fitted them with 33 bullets, first in .333 and then in .338. - Dan

As an addendum, I seem to recall that they were the same ballistically as the 338 win Mag. - Dan

They were equal only due to the powders that were available at the time. With today's powders you can improve on the 333OKH mags.

I don't know why you would want to but to each his own.

Mike