My point is that you are providing them with 4x the survey so should insist on significantly more than the additional 10% of work unless you see a survey business as some kind of charity or public service. In my opinion a 10% additional charge wouldn't be worth the 4x more liability. And if the client did have some interest in a full survey you'd probably be leaving money on the table with just a 10% increase.
The point is to make them pay 90 percent of what a full survey would run them...........no matter what. Not giving anything away.
The liability is basically the same whether you set the remaining corners or not. So put all that potential risk into the cost of locating just one corner.
If they don't like your price, let them call around. You don't really want to work for that kind of client anyway.
I hear what you're saying and completely agree. They need to pay for all work to get the job done properly. I'm just pointing out that if they already agreed to pay for the full 90% price for one corner, they may be willing to pay even more than the 100% for the whole thing. For this reason I prefer a fixed fee cost structure when at all possible. A service is worth what someone will pay for it, I think too often Surveyor's undervalue what they are providing.