In her work on Cultural Influence, Julia Middleton talks about the concepts of core and flex.  

Our core is those things that are most important to us.  Our moral values and beliefs.  Flex is the amount we are prepared to change.

Although Julia uses the terms in relation to cultural intelligence they have much wider application for influence.  Even within our own cultural settings the tension between authenticity and effective messaging exists.  

This article by Nick Enge reinforces what Julia was talking about.  If we move too much from our core we lose our authenticity but if we can't flex our message it won't resonate with those we are trying to influence.

Understanding our own core and flex and working out how we can maximise flex in others without compromising their core values is the art of mutually beneficial influence.