It will be nice to have not a globally defined shadow style but customizable one for difference components and different situations.
For example in my case I'd like a different shadow color for different kind of informative messages wrapped in a Paper
component: red
for important information and green
for just some not that important information. Here is a screenshot of desired state:
The shadows are generated thanks to that file shadows.js. Material-UI expose enough customization power to achieve what you are describing. You might like that thread https://github.com/callemall/material-ui/issues/6130#issuecomment-312686660.