The best extension I’ve run into related to multi-newsletter (or simply newsletter groups) is the following one:
Multiple newsletter lists in Magento
It’s free and works like a charm. It allows us to easily create newsletter groups from the backend (Newsletters » Newsletters groups) and then modifies the newsletter blocks on the website to add more checkboxes, so the customers can check on the groups they want to sign up. After that, we can send/exports newsletters filtering by these groups.