While you cannot remix your own images, there is a fairly simple method for duplicating your own images without manually recreating every tag.
1. Copy Tags
On your profile, open the image you wish to duplicate. Click the pencil button to edit, and in the editor, right click. Select the 'Copy Tags' option.
2. Re-Upload Image
On the Create page, re-upload the same background image.
3. Paste Tags
In the editor on your new image, right click again. Select the 'Paste Tags' option. The placement, icons, and content of all your tags will be duplicated on the new image.