Is it possible to locally replace a website's Javascript when the page loads?

I am not talking about using an add-on such as greasemonkey to inject new javascript. I'm talking about providing (possibly a browser extension of some sort) a custom js script to be loaded instead of the one that the page provides.

Example: Page has <script src="script.js"></script>

I would like to tell my browser to run X code instead of what was in script.js

Thank you. Sorry if the question is not very clear.