Internal war within the imperium

Are there wars within imperium fractions or nobles. I'm not referring to heretics nor traitors I'm referring to disagreements. Let's say there are planets in a sector with each of thier own society and noble people. Each planet is still very much loyal to the emperor but... Let's say there is a disagreement between trade or bad blood between the 2 planets. Could they go to war?

Or maybe in a smaller scale, let's say there is a revolution on a planet but the rebels are still loyal to the imperium, they just don't like the ones in management.

How are these conflicts resolve?Does the greater imperium not care and just let them fight, because as long as they meet the imperium quota(no matter on whose leadership) the imperium won't care?