How do you track, measure and manage stakeholder relationships?

I've been thinking a lot lately about stakeholder relationships. I would like to use a framework to evaluate the desired state/mix of stakeholders including sentiment compared to the stakeholders that we are currently engaging. The outcome of this evaluation would be a plan to fill in the identified gaps in our relationships. 

Maybe a matrix that has client sentiment/NPS (detractor, resistant, neutral, supportive) and key to success (a.k.a. do you need them). No one should be a detractor of course.