That often confuses people because it will make you switch gears between differences while crafting your story. That usually makes your point more diffuse and takes away from the power of your story. On the other hand, it often does make sense to have one overall story and re-use it for different audiences.
To make this concrete and tangible and also to explain the concept to others, I often use the story-audience matrix. It is a really simple matrix with the different audiences at the top and the different chapters, modules, parts of the story (or whatever you’d like to call it) on the left. By creating a matrix like this, you will create an overview of the two main dimensions: the content you have and/or will need and the audiences for that content.
I will often add a final, third dimension by making the ‘dot’ in the matrix smaller or bigger. The bigger dots will mean I will need to ‘full story’, the smaller dots will mean I will use a concise version of that chapter.
For example, you don’t want to bother the board will all different examples within your project, but do need to present them the full business case. On the other hand, you can not present anything from the business case to an external audience as it might be confidential, but you do want to take them with you on the journey that has been the development of your project (history).