The Remington 760 will work, 7600 is better. Both are equally strong, but the 7600 has fewer, larger locking lugs on the bolt. I consider it more reliable. So did Remington, and that is why the improved 7600 replaced the 760 in their lineup. Both are good to over 60,000psi. The modern Winchester/Browning 1895 is good to over 60,000psi, while the modern Marlin 1895 is rated about 42,000psi, and the modern Winchester 1886 and 71 are good to around 50,000psi. Older guns, and other Winchester models rated for much less pressure. Browning BLR's and BPR's are chambered in belted magnums OF STANDARD LENGTH (i.e. 7mmRM and 300WM) and rated above 60,000psi, like Roklok stated. None of the above rifles would work for magnum LENGTH cartridges like the 375 H&H and similar due to action and magazine length.
The Browning/Winchester 1895 has been converted to 375 Hawk, 375 Whelen, 411 Hawk and 400 Whelen. I prefer the Browning due to the half-cock safety. The Browning 1895 in 375 Hawk and 411 Hawk were used as stopping rifles on Alaska's biggest bears by the late great Alaskan guide Ed Stevenson, especially the 411. Of course what he could do with a rifle under pressure and what I can do with a rifle under pressure are probably 2 different things. He used 350gr-360gr .411 bullets at over 2300fps and over 4200fpe to great effect on big bears. He was also fond of using the Browning 1886 in 45-70 with a 400gr bullet at around 1900fps on the big bears. In retirement, killed maybe his last bear while walking his dogs in town with a Marlin 1895 Guide Gun in 45-70. The bear attacked the wrong dogs. The only thing stopping a charge from an animal that size is a CNS shot, and a person could do a lot worse than having fast handling levergun in those situations, as long as the gun is powerful enough. Again, Stevenson's skill level, experience, and knowledge of the animals made him able to do things with a rifle in a charge situation that a novice could not. Earlier in his career Stevenson was mauled after being attacked by a 10 foot grizzly. Protecting his client from the unwounded bear, he was only able to get off one shot to the chest with his 375 H&H bolt action before the bear was on him. The client hunter saved Ed by shooting the bear when the bear was on top of Ed. After this incident, Ed started looking for faster handling and shooting rifle options, and he settled on the lever actions. The 411 Hawk and 400 Whelen will also do over 2150fps with 400gr bullets for 4000fpe. This matches the ballistics the 450/400 made its fine reputation on with everything from elephant on down. While the 450/400 is not considered a stopping rifle for tough African game, it has a well deserved reputation as a fine hunting rifle for ALL African DG. You can load modern 450/400's hotter, whereas the 400 Whelen is maxed out at 400gr at 2150-2200fps. Still, pretty impressive for a 30-06 case. I have a Browning 1895 in 30-06 and I am looking for a gunsmith to convert to 400 Whelen. JES was hesitant to rebore the 1895. The fixed box magazine must be modded to reliably feed the bigger rounds.
I have a couple Rem 7600's in 30-06 and I have located a smith that will re-barrel to 400 Whelen, but will not do the magazine/reliability work. I can to that work myself. These 7600's were made by Remington in 35 Whelen. This is a very powerful round in it's own right, and this 35 Whelen pump action was popular in AK for bear hunting/protection. The 35 Whelen is very similar to the 9.3x62, just .008 less diameter than 9.3. I wish I could find a gunsmith to open up the bolt face of the 7600 for belted magnums, and beef up the extractor. For me personally, the pump action is probably the fastest accurate second shot of any magazine fed action type when firing heavy rounds. Almost as fast as a double rifle for me in heavy recoiling calibers, probably owing to the fact that I grew up using pump action 12ga's for wing shooting since my teen years, and still do. Another advantage of the 7600 is that you can have a gunsmith make extra barrels for the same gun, and you can switch barrels in the field with a few tools in about 15 minutes. Not exactly considered a takedown model, but you can easily switch a Remington 7600 from a 30-06 to 35 Whelen to 375 Whelen to 9.3x62 to 400 Whelen in minutes in camp, pretty handy. I hope to have a 30-06, 35 Whelen, 375 Whelen, and 400 Whelen set made for one of my 7600's. I think a 35 Whelen for PG, and a 400 Whelen for DG would be a perfect combination for Africa. Bob "35 Whelen" Nelson on this forum loads 300gr bullets in the 35 Whelen bolt action to between 2400-2500fps.
I also have a Browning BLR in 7mm RM and I am looking for a gunsmith to re-barrel to 416 Ruger or 458 WM. I saw a BLR converted to 416 Ruger on GB. This rifle was new and listed by Aria Ballistics, who did the conversion. Aria Ballistics is in the process of moving to another state, and will probably do this work for me when they get settled. I think of all the heavy pump and heavy levergun options, the BLR is probably potentially the most reliable with heavy loads due to rack and pinion mechanism between the bolt and lever giving very powerful mechanical advantage for extraction if needed. Same mechanism as used on arbor presses.
So there are a few leverguns and pumps that will work in calibers power enough for hunting African DG. Cape Buffalo have been taken with Marlin Guide guns in 45-70 (which I would not do, even though I own one and I like the rifle), but I would feel a lot better carrying a lever action or pump in 400 Whelen, 416 Ruger, or 458 WM. If I ever get one built, I will let you know it turns out.