MacKC,
The original Browning/Winchester 1885 was at it's best reliability with rimmed cartridges. They have been adapted of course, for modern rimless cartridges.
I've not seen an 1885 chambered for 7mm Remington Magnum, but am sure they exist. There should be no problems with receiver strength, barrel shank thinkness, etc. My only question is that of extractor reliability on a dangerous game rifle such as .338 Winchester Magnum.