I found the answer elsewhere - using the term "duplicate" instead of "copy". This worked, so I'm including it here in case anyone else uses the wrong term!
"Yes. Click on the [Download/export] button (lower left of tree screen). Save as GEDCOM or FamilyScript. Click on [My Account] button (upper right of screen), then click on [Create or import new family]. Now click on [Import GEDCOM or FamilyScript]. Click on the [browse] button and select the file you downloaded, then click on [Import]. You can rename the new tree on the My Account screen.
Answered Dec 15, 2016 by DanUgrin"