Yes, you can definitely add new buttons/services to your site, using a couple of filters. I’ve put together an example for Print Friendly here. There’s an older, but similar example for Facebook Messenger here.
Basically, it’s two steps: 1) add the new service to the list of available buttons; and 2) update the output URL for the new button.
If you add filters to your site, please practice safe coding and make sure files are backed up.
A note if you are using the SVG icon options: the icon will be added to your button properly, but I’ve discovered a bug which is not getting the correct CSS class for the buttons when using the SVG icons, so you will need to temporarily add your own CSS for the button background color. I’m adding a fix to the plugin.