If you mean you want to set custom metadata for files that you could read via the API without downloading the file content, then no, this isn't currently possible, but I'll be sure to pass this along as a feature request.
If you mean you want to set metadata specific to certain file types though, that would be stored in the file itself, you can download the file, edit it as desired, and upload the new version.
If you're using an official SDK, there will also be corresponding methods for these endpoints.
We love to learn from the educators who use Dropbox. Whether you teach kids, teens, adults or a combination of all three, we want to know what apps and integrations you use with Dropbox to help with teaching. Which of the ones below is your favorite, or most used tool?