Yes this is possible by embedding more than 1 Clipchamp button and setting a different upload target per button instance.
Please note that in our WordPress plugin, all embedded Clipchamp buttons can only upload to the same upload target, e.g. the same Google Drive folder if Google Drive is the upload destination you set.
However implementing the API manually without making use of the WordPress plugin allows you to define a separate upload destination per embedded video button in the code of each button instance, e.g. so you can send user videos to a different folder on Google Drive per button instance.