Press Alt+Shift+D to duplicate the current tab (Option+Shift+D on Mac). Shortcut is configurable.There is an option to open new tabs in the background, enabling that option requires more permissions.
There are additional shortcuts as well. You can configure and use all of them at the same time.
- There is a shortcut to open the new tab in a new window.
- There is a shortcut to pop the current tab (or multiple highlighted tabs) out to a new window.
- There is a shortcut to open a blank new tab to the immediate right of the current tab (i.e. instead of all the way to the right).
There is a Firefox version available as well: https://addons.mozilla.org/addon/duplicate-tab-shortcut/