There are several ways to leverage an existing email list to get more email addresses and/or customers.

First, I'd make sure that your emails to these folks are optimized for sharing. Include a call-to-action at the bottom to share the content/product/offer with their friends by posting to social media or forwarding your email.

A referral program is another great way to incentivize people to share. It's tough to give more specific suggestions without knowing what type of product/service you have and who your audience is, but try to think about how you can provide additional value to your customers if they sign up X new customers or share your content with X friends.

If you're using content marketing as a way of attracting leads, you can run a test where - instead of filling out a form to download your content - they have to share the content on social to unlock the download (called "share-gating").

If you do set up a referral program, using Custom Audiences on Facebook is a great way to target ads to your existing customer base - use this and email marketing as your channels for growing awareness of your referral program.

Hope this helps - happy to hop on a call if you'd like to discuss further!