Double rifles are re-chambered and re-bored all the time, and some such conversions are very common. Twenty years ago .400/.360 Purdey doubles were quite common, but are much harder to find today. Most have been re-chambered to 9.3X74R. Likewise, many .400/.350 and .350 No. 2 rifles have been re-bored and re-chambered to 9.3X74R. Such conversions don't make much sense today because the old cartridges are as good as they ever were, and components and loaded ammo are available now. However, it makes a lot of sense to re-chamber in order to get rid of a really dumb DR caliber choice - like .458 Win Mag.

A fair number of the older doubles have been wildcatted just to clean up badly pitted chambers. A fair number have been re-bored to a larger caliber because the bores were shot out.

I've seen the very conversion that you mentioned - 9.3 to 9.3 with a .375 Flanged Magnum case. This rifle was rechambered (and reproved) to use the .375 case because the 9.3 chambers were badly pitted. Otherwise, that conversion doesn't make sense because almost nothing is gained.
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