When should contracts be renegotiated

So this is more of a question than a statement, but I am starting to wonder when I should consider changes to the script and budget as motivations to insist on contract renegotiation.

Two recent conversations led me to this post.

The first was a conversation with a production manager who told me that one of her newest lessons came from a Tech Director (TD). He told her that if the budget of a show is increased, he always insists on an increase in pay. He logic was this; When he signs onto a project, he is agreeing on a certain amount of pay for a certain amount of work, namely as much scenery as can be built with the budget designated. Production managers and producers often decide, if a set estimate comes in over budget, to redistribute money, and increase the set budget in order to get the set desired. Unfortunately, this TD contends, that means more work for the TD, as more money means more scenery. This TD insists on renegotiating his contract if the budget has changed, because this means he is being asked to build more for the same pay.
This is something, in props, that I would never have considered. Often in my work, the more money I have, the easier my job becomes, because I can spend less time looking for the absolute best price possible.
The contract renegotiation that this TD spoke of seems very do-able, since in most cases the budget is listed in the contract. It is not hard to explain that a changed budget, changes the written terms of the contract. Having this in mind has convinced me to make sure all future contracts explicitly state my budget.

The second conversation I had is a bit trickier and also a more common problem.
A costume designer I regularly work with told me that she was frustrated with a current project. After she had signed her contract, the script was edited. In the new draft there was a huge prosthetic costume/makeup effect that had not been included in the first draft she had been given. She had taken a low paying show with the understanding that it was also an easy show. Now it wasn't an easy show. She felt bitter, stuck and taken advantage of. The conversation made me wonder if maybe I should think about asking for a clause in my contract that states that the pay and budget are based on the draft of the script that I had been given to review. I want the ability to reopen conversations about budget and fee if changes in future drafts significantly alter my workload.

These are just thoughts right now, but I would love to hear your thoughts and experiences. Do you have specific clauses you ask for in contracts? Have you even had to alter a contract based on changes to the script or to the design?