Yeah that makes sense because S3 provides a single URL for a file to be uploaded to. You can still provide a UI to receive multiple file references from the user, but then you need to do a call to a controller that will return a temp url for each file. You then post the individual files to those urls.
When the form is submitted, submit a reference for each file to your laravel controller so you can manipulate the upload and store then where you want them to be on S3.
I use dropzone.js to give me the appropriate hooks, but am sure there are other options available as well …