Instagram has all but killed off Snapchat by this point, and it's got a lot to do with the strength of its stories and live video features. With the latest update to version 24, a new 'Request' button has been added to the comments section of live videos to be added to the stream.
You can ask to join by tapping the icon with two smiley faces, at which point the presenter will get a notification allowing them to approve or deny your request. If they accept, you'll get a moment to prepare before the video splits in two and you're live alongside your friend.
The original presenter can also invite friends who are watching in the same way by tapping the double-smiley button. Anyone can leave at any time, so it's no problem if you just want to stop by briefly and say hi. As with any live video, you can choose to share it to your stories or discard it when you're done.
The new feature is part of Instagram v24, which you can update to via the Play Store or download manually from APKMirror.