Not super sure for Tailwind CSS how would it look, but indeed Laravel mix can create multiple files, you only need to create the appropriate resources:
For instance, I have a vendor.js file and an app.js file both in the resources/js folder. What mix is doing here, is creating a vendor.js file and app.js file in the public/js folder.
mix
.js('resources/js/vendor.js', 'public/js')
.js('resources/js/app.js', 'public/js')
.vue(3)
.postCss('resources/css/app.css', 'public/css', [
require('tailwindcss'),
])
.version();
You can name the files whatever you want, and Laravel mix will compile it to the corresponding name in the public/js folder.
Surely the CSS files could be a similar path, but since Tailwind has its own compiler, I'm not super sure how would that work, however, I wouldn't overly bother about the CSS file, it's possible it won't be replaced as much.