As mlesemann said, they can demand anything they want in their contract.
I've heard of really odd contract stipulations where they only bathe in a particular brand of bottled water to simple demands of particular personal assistants and/or makeup people. If that can be in the contract, anything can.
It's up to you to determine whether the cost is worth the benefit of having that person in your production.
For example are they able to have a clause that says they have veto over who else is cast in the film?
Yes they can.
Can they ask for 10% of the gross box office takings? Yes.
Can they ask for final cut? Yes.
Can they stipulate that they will only be involved if a particular crew/cast member is in the production? Yes
Can they have all decisions routed through them for all casting decisions? Yes.
Can they ask that they travel without anyone else, in a particular type of vehicle? Yes
Can they ask for a particular class of accommodation? Yes
Can they ask for a higher pay rate than scale? Yes
San they ask???? YES YES YES
If you say yes. Will they get it? Depends on the negotiations.
A contract is simple a written agreement of what both parties agree to. The contract scope changes depending on the terms.