Add more field on WordPress media upload

not without creating your own custom form. There are 2 ways to achieve this,

1. uploading attachments in the post editor, In your post edit page you can create a custom metabox which will allow you to enter custom fields for your posts. When you save your post, you can hook into the backend saving process using the save_post action and look for your custom fields in the $_POST array of submitted fields. You can also capture the attachment id in case you want to attach your custom fields to the attachment itself.
2. Creating a custom admin page with am uploader, alternatively you can create a custom admin page and setup your own attachment uploader and custom fields. See this little video tutorial for more details.