To be honest, there are very few Big 5 cartridges that are suitable for anything else all over the world.
the smallest of the DG calibers would be the obvious choice, that being the 375, 9,3's etc.
But they are rubbish
Once you start looking at 458's and up in bolt or double they become more specific to certain game and certain situations.
If you are looking at a 3 gun battery, i would choose any of the 6mm/6.5mm's as a small gun, a 300wm as a medium and a 416/458 as a DG gun.
If you get it right, you can have all three in mauser m03.
Where do you live? i need to come give you a smack across the ear for that one...
i have a 243, 300wm and 416rigby as my regulars, the 243 will cover all animals up to lechwe size with ease, perfect medicine for crocs too.
the 300 will do all up to lion, leopard, eland etc.
the 416/458 will cover buff, ele, hippo and anything smaller that you happen across.
there is very little worldwide that you couldnt shoot with those 3 calibers. you could always swap out the 416/458 for a double in 450, 470 or 500 and it would be much of the same.
there will always be occasions when a specialty rifle may come in handy, but these three will most certainly do it.
as a note, i would swap the 243 for a 6,5x55 personally as the heavier bullets will be advantageous.