One thing I have found helpful is to ask how the producers plan to pay for changes that make things more expensive? I give them a very frank estimate of what things will cost and why. If they don't want to hear it... then offer cheaper options... but in the end, things we do cost money...

Use tools like saturation.io that make it easy to make changes to communicate where you can adjust the budget as well as what action you should take.

The director's and producer's ability to adapt is key in this equation. On a Sony Entertainment film I worked on, the writer and director strongly agreed an additional scene was needed for the story, despite the budget being locked by the studio.The director chose to cut the use of a crane and picture car for an establishing shot. Instead, he blocked the scene (w actors) and figured out a different, more intimate way to film it, which worked beautifully and covered the costs for the additional days of filming. Often there are smaller script changes requested by star talent that require creative budgeting, namely, using the buffers tucked away in various line items and re-allocating those monies to cover the approved script changes.

I ask why the changes need to be made. Most times there are ways around it to still stay on budget, if not, you have to go back to the investor. Or, it doesn't get finished.