I know I'm going to get flamed on for this, but I think no harm would come.
I have a Marlin 375, and an original Winchester Hi-Wall in .38/55. Keeping brass seperated is a chore, and I was wondering about having a gunsmith running a .38/55 finish reamer down it.
The .38/55 is only a few thou deeper than the .375, and there would be no outward indication that it had been done. I shoot the same load in both rifles, and have shot, ( I probably shouldn't admit this,) .38/55 in my .375 without any signs of pressure.
But I know the extra length of the .38/55 is taking up leade. If I deepen the chamber in the .375, I could then shoot .38/55 in both rifles. Opinions? Thanks, Mike

Check out this thread. Be sure to follow the link in post #8.

If you plan on shooting cast bullets in the 375...(many in the 245-265grain range), you will have a pretty hard time as the twist in the 375 is nominally 1/14 and the 38-55 is nominally 1/18...I've got a friend that loaded cast in the 375 and it will strip the lead as it starts into the fast rifling...good luck...As far as the brass, 38-55 brass will "normally" load/shoot in the 375, as long as you don't go over the overall length of the 375. Shrps74