These sorts of things are more common in RSA and other countries with game ranches because of the private ownership of all the game. Cutting both ways, some clients want to upgrade their trophy already shot each day as they see a bigger one, alternatively the PH is nudging the client to shoot everything possible.
It is the above factors that then leads to a very tacky conversation from all parties at the end of the hunt. "Lets make a deal". That can occur from a sleazy client welching on their agreed package, or it can be a tactic of the operator/PH saying "shoot it and we'll figure it out later, or I'll give you a good <not disclosed> price while you're on sticks".
Never had to deal with this because I've never hunted a place where the PH/Operator owned the game. In places like Zim and other similar frontier hunting regions they will tell you before the hunt what they have on quota. They will ask you prior to arrival if you want any or all of their quota species added to your license free of charge. Once on the ground, you either shoot them or you don't, but there isn't an opportunity to shift prices or add animals beyond that because the quota is what it is and the quota is property of the government.
Not saying Zim is better than RSA, I'm just explaining that the negative to RSA especially is the OPs scenario can happen, and in many other places it cannot.
The plus to RSA is its business and conservation model is one of the two best success stories on earth for the restoration of game species. (the other being USA) The RSA business model of private ownership of game is why they have the game they do, that's the plus. The minus is the OPs question which does/can happen there.
