The following plunkr code does almost exactly what I want to do:

https://embed.plnkr.co/plunk/l63VJk

The last section titled "Can I Upload Multiple Files" is what I'm focused on. It allows me to select multiple files to upload, but ONLY if I select to upload them all in one go (clicking "choose files" then highlighting multiple files and clicking "open"). I want to be able to upload a file, then click choose files again and upload more files, without the original ones being overwritten.

How would I go about doing this?