This is a situation I have thought about many times. I wonder if it is better that in say 416 rigby the first bullet is solid and the second soft? In which order do you who have had such situations put the bullets in the barrel?
In the time when the only option was cup and core soft point this was the holding doctrine.
Clients were advised: first shot soft point to make maximum damage, and when buffalo turns, next place a solid.
Either in brain if charging, or diagonal shot if he is running away for maximum peneteration to reach vitals.
Risk:
Solid can make exit wound and wound a second buffalo in a herd.
Then you will have situation to deal with two wounded buffalos, and then to pay for both of them.
So when shooting solid, a care should be taken about surrounding situation and other buffalos around.
Modern solution.
Use swift a frame, first and second shot on buffalo. Fire and forget.
My PH on buffalo hunt suggested exactly that. It worked for me. Good penetration and no exit wound. swift a frame performed perfectly. Deep penetration and no exit wound
Having said that:
my next PH during our elephant hunt, in buffalo country, when we were hunting other animals, with optional buffalo around told me, when buffalo is around, (as it was) have soft point on top, and solid as second round. So, I was shooting large plains game with softpoints, with second round in magazine being a solid. After first shot on plains game, I wold just top up a soft point on top of solid.
In conclusion, both theories are still alive, and in use.
But majority of modern Ph for buffalo prefer premium soft point ammo like swift a frame, or TSX or TTSX, and forget about solids.