The OP is getting solid advice and accurate disclosures about doubles on this thread, particularly the sage advice and options from Redleg.
I’ll not beat a dead horse on double aesthetics or brands although I do like Heyms and pre-war British stuff myself.
So ballistics: a 375HH flanged and a 9.3x74r are both pretty common and “inexpensive” double rifle calibers. They are both built on small frames that cannot accommodate dangerous game calibers. Both are adhering to the original bullet weight and velocities to regulate in a double rifle so their versatility is hampered compared to their rimless magazine rifle twins: 375HH belted and 9.3x64 brenneke. By all means, buy a gun in one of these calibers and use it for hunting in the US and for Africa, but these aren’t your dangerous game cartridges of choice, especially when in a double rifle “light load, standard bullet” configuration.
A 450/400 is a significant step up in performance as a dangerous game double rifle caliber just as it’s rimless twin, the 404 Jefferey is a better Buffalo gun than a 375. Do not be deceived by the relative velocity and energy similarities between a 375 and a 450/400. 1.) the bigger hole does matter, professionals have noted this for more than a century that the 40 cal bullets are just more effective. 2.) the charts that make them seem similar are assuming a standard 375HH versus a vintage 450/400 with a 350gr bullet. Modern doubles are shooting 400gr and 450gr bullets from a 450-400 and it’s quite a step up in performance. Also, the sweetheart recoil of 41lbs from the 450-400 is quite a bit higher with the 450gr bullet, but still more manageable than the next step up in dangerous game rounds.
In practicalities, you will own a 375HH magazine rifle for US and Africa and you will buy a dangerous game double rifle. You will kill dangerous game half the time with the 375HH because you were chasing plains game with it when you happened upon a Buffalo. Also, you will kill plains game with your 450-400 or larger double rifle when it presents itself too, just with less success and fewer opportunities.
We can wax poetic about multi barrel guns with all the options but the reality is you can buy 4 good used rifles for the price of one new rifle with all the caliber barrels you want. I’d never go to Africa with less than two whole guns anyway, so just buy more guns.
No one has ever been called an idiot for buying a 375HH magazine rifle and a large bore double rifle. It’s a classic setup. In the end, the double rifle gets 5% of the use of the 375HH bolt gun, but it’s great to have both.
My 375HH has killed more animals than my 470NE double rifle has fired rounds of ammunition. I bet that’s a common situation. Let that sink in as you decide which to give priority.
Since you want a double too, get a big one, a 375 flanged or 9.3x74r is a great specialty gun for a fellow that has a broad array of guns, but it isn’t the first double most people would opt to own.
