Check For More than One Tag at a Time

I currently am working with an in-progress site that we’d like to be able to let our users search through posts using the tag system, but what we’d really like to be able to do is have it so they can use two or more tags at the same time to better define their results and get to the exact post(s) they need.

Is there any way to do that with tag groups? Everything else about this plugin has been perfect for our needs, so I’m really hopeful! Thank you!