Improved "Notification" Options?

I know there is already a "notifications" system within Heartbeat, but I'm finding that some of the notifications I receive take me to the thread and not the specific reply/mention within the reply. I'm wondering if there is a way to improve this experience. Like have some kind of feed with only new messages and replies.

One of the things I love about Circle's reply/mention notifications is that I can open each up in a new tab and easily hit every one of them, making sure I don't miss any messages. Are there any other ways of getting replies and mentions that would improve on the system currently available in Heartbeat?