Building double rifles on shotgun actions has a lot of variables. Some are far stronger then others. More strength can come for a stronger design or in some cases, very high grade steel and in a few cases, from both. Also the caliber is important. Power can be available by volume instead of pressure, which is why a cartridge like a 9.3X74R if often preferred over many more "modern shells. A 348 Winchester of in your case a 375 Winchester are not wimpy, but are a lot easier in a break-action system then say a 308 Winchester or a 7MM Mag, and I doubt anyone can't see that a 9.3X74R has more power available despite the lower pressure. So pressure and the pressure curve of a given shell can be more important them simple power.
Anyway there is no easy answer to your question. It depends of what shotgun you start with, and in the case of some actions, their heat treatment was all over the pace in the days they were made simply because having it strong enough for a shot gun shell was the only goal. Having it 3X stronger or 5X stronger, or .5% stronger then it needed to be was enough in every case and none of them were considered to be used for a rifle, so you may get a shotgun that is excellent for a build and then go get another one of the same make and model and find it's too soft for the same exact build you did last year. Some of the guns were held to specific standards in their metal processes and alloys (many of the Japanese guns were ) where others were made "strong enough for any shotshell" and nothing else was considered (Spanish guns often fall into this category)
There is no pat answer for the simple question. Overview ....... Yes is possible and can be done very well, but you must start with a solid and strong action.
