Naturally, power/interest is not the only approach to stakeholder prioritization and engagement.

The concept of Stakeholder Salience was proposed by Ronald K. Mitchell, Bradley R. Agle, and Donna J. Wood in an article for The Academy of Management Review in 1997. 

The authors proposed a Theory of Stakeholder Identification and Salience in response to the many competing definitions of ‘stakeholder’ and the lack of agreement around ‘who and what really counts’ in stakeholder management.

For them, stakeholder priority is derived from three independent factors they defined as follows:

• Power
  A powerful stakeholder has the means to impose their will on the project. 
• Legitimacy
  The perception or assumption that stakeholders’ actions are desirable, proper, or appropriate. 
• Urgency
  The degree to which stakeholder claims call for immediate attention.

The interaction below gives some insight into how the authors perceive each stakeholder category.

Note that each of these variables is binary, in that you either have it or you don’t; whereas our representations of power and interest occur on a continuum (you can have degrees of each).

The stakeholder salience model is also silent on whether a stakeholder is positively or negatively predisposed to a project, and does not propose specific engagement methods as a result of each stakeholder classification.

That said, Mitchell, Agyle, and Woods’ work is well worth exploring as a valuable complement to better understanding stakeholders and developing your own ‘best practice’ in this space.