I've done agile projects where the client was a big corporation. There was a fixed budget and deadline, but we specifically reserved some of that time/money for unspecified work at the start of the project. In the latter parts of the project we could then prioritise the work that was deemed most important by the client once they'd already seen the work in progress.

I suspect it took quite a bit of work by our project team to convince them to work this way. But it's really great if you make it happen.