How do I add a taxonomy vocabulary to more than one menus with the taxonomy menu module? I'd like to have two different menus based on the same taxonomy vocabulary, but the taxonomy menu module only lets me choose one menu to add the terms to. 

Can I somehow add the same terms to more than one menu?
Try this: https://www.drupal.org/project/taxonomy_menu_block

Otherwise, you can use views to create blocks with links from a taxonomy vocabulary.