PMing Members will still be reliant on Email since you won't know about the PM until you visit the site.
We have removed the social integration from this site for many reasons one of which is the requirements / information and ability to interact with people that come from popular social networks changes all the time. It is actually a complaint a lot of other site owners have as well. A good example of that… it used to be that you could use an API to send a notification to someone on FB about your site but they changed that a couple of years ago.
One way I have thought about was to create my own mobile application that sends out notifications to a user that has the app installed. While this could be effective it will of course rely on the Member installing and using the app on their end. While on our end we would constantly need to ensure it works across all mobile operating systems.