This extension enables you to highlight (select) parts of posts and quote only that highlighted part. It works similar to the quoting function in the topic review when you are on the posting page.
Once you have selected a part of a post, a floating quote button appears near your cursor. Clicking that new button does the magic. When quick reply is enabled, the quote BBcode is inserted in the QR textarea. Otherwise, you'll be taken to the posting.php page just like with hitting the regular quote button but with only the highlighted part of the post.

A second feature is multi-quoting. You can tick a new multiquote button on each post. When you have selected one or more posts to quote, a floating quote button appears in the bottom right corner. Clicking that button takes you to the posting screen as with regular quoting but now you have multiple posts quoted in your message textarea.