Uberti "Highwalls" have been chambered for .348 for some time now; Buffalo Arms in ID used to sell them (I think they were imported by Cimarron). They seem to work OK.
I just did a quick buzz thru both of Cambell's "Single Shot" books and found no mention of the .348 as an 1885 chambering, even in the cartridge test "mules" that du Pont kept to test loads. But I would NEVER rule out the possibility of a factory "one-off" with an M71 barrel installed by a Winchester employee on a factory spare reciever. Make you a good "hammer" for hard-to-kill things....
I'd say there's NO reason "why not" IF you're a handloader. I imagine that C.Sharps (among others) would make you one (alhough I can't tell without calling them; their web page that lists calibers available is perpetually "Coming Soon"!).
