Recent updates in phones' OS provided tools to help us control the vortex, but they aren't enough.
I think what would be really useful is a way to group the different interactions and people of different social group and time box them. For example, if someone from work contact me, I'll only see the notification between 9AM and 6PM. If it's a friend, it's only after work. Unless it's a close friend, who could contact me anytime.
Basically a way to group notifications by context: work, fun,etc