Take the story of Joseph, Genesis 37-50.
#1 A feel good hero
A story inspirational enough to inspire Andrew Lloyd-Webber. Is his 1970s Disneyfied reading the true meaning?
#2 Joseph a christ
Or what about the classic interpretation of Joseph for most of church history - that Joseph is a Type of Christ, a beloved son who suffers and figuratively dies, but who is raised up to feed the world? In this, telling the dreams is revelation of the way that he'll lovingly provide rather than arrogance. Jesus says Moses wrote about Jesus...
Or, a more modern reading, that it's a story about either (three variations on 'Be Joseph'):
#3 Suffering in general
People might mean things for evil but God is always working for good?
#4 Providence in general
Similar to the previous, with an encouragement that you might be falsely accused etc but nonetheless finally vindicated. Both #3 & #4 major on the summary verse in 50:20 about the brothers evil intent and God's good plan.
#5 Lessons in Leadership,
With warnings to not to be arrogant (even if you're right) and to flee temptation and so rise to greatness like Joseph, but also to plan for the future, hear God etc. Application to leadership is of course possible from each of the above options too - from a search for the hero inside, to the kind of leadership we see in a christ, and how to face suffering and hardships etc.
Should we teach all of them? Some of them? Only one of them? Or something else?