I have read a few times where folks have stated they shoot 375 Win from their 38-55 Marlin 336.
There is a difference between the two chamberings. I have a .375 Winchester and my Father has a TC Encore in .38-55. We have shot both cartridges in the Encore with no indication of trouble.
To better understand why people get away with shooting the .375 in the older .38-55 rifles read Ken Waters Pet Loads article on the .375 - 1-79 and the Pet Loads-Update, 1-83. The .375 case is shorter by design. Pretty clever design thoughts went into this cartridge.