"...every inflection and movement implies a status... no action is due to chance, or really 'motiveless'... All our secret manoeuvrings were exposed" (Keith Johnstone 33).
Use Keith Johnstone's concept of Status to explore character interactions.
At any point in the process
I particularly enjoy this exercise as a way to explore various sides of a single character when things are feeling stale.
Status, put simply, has to do with tiny interactions between human beings. These interactions are attempts to get what you want. They track on a single, easy-to-understand scale: Social Status. Each behavior can either raise or lower the social status of the behavior or the behavee. These behaviors can relate to what is said, how it is said, gestures, body position, speed, pitch, etc. There is a difference, therefore, between looking someone in the eye and staring at the ground. There are also a differences between someone who uses complete sentences and someone who does not.
Where it gets interesting is when you can see that the "boss" or "king" doesn't always have the high status we assume they would have. Think of the "fools" and "jesters" in comedies. A more modern example might be the character Peter Gibbons (carefree employee) in the film Office Space. These status interactions are small, constant, and ever-changing. This exercise asks you to utilize them in service to your writing.
NOTE: I recommend getting your hands on a copy of Keith Johnstone's book Impro, as there is a great textual example on page 38 of his book that analyzes a scene from Moliere's A Doctor in Spite of Himself. It quickly illustrates one way that this idea of status is -- and can be -- employed in writing. Seriously, just go buy or borrow a copy of Impro now, it's that good.
Hopefully Status has been an eye-opener for you. I also hope that your scene was an interesting exploration. Perhaps you found something new about your characters. Perhaps the scene became more interesting. Perhaps it was a complete failure, but demonstrated a clear direction you need to take on subsequent drafts. At any rate, I hope that employing Status for the purpose of writing has caused you to think about character interactions in a different way.