My website has currently 3 CSS files that are automatically included as a part of the website and I do not have access to the source i.e. index.html
For duplicate CSS definitions, the last definition will have precedence.
If the added css4.css file is actually referenced after the "3 css files that are automatically included", then the css4.css file's definitions should override the prior duplicate definitions from these other files.
If you are not seeing the results that you expect, use the "view source" option of your browser to confirm the sequence in which the CSS files are referenced. Also use the "Developer tools" of the Chrome browser or the "Firebug" add-on for the Firefox browser to find out how the browser is interpreting the CSS definitions to yield a result that you did not expect. These tools should provide insight to your problem.