In addition to war, religion, and economics, it would be neat to have a Space Stage dynamic for culture, beyond merely "I'm a Zealot, I hate everyone!" and what have you. It would incorporate a little more of the empire's properties and make background changes; a little more flavor if you will.

The clash would be an alternative method of gaining systems to augment what is already there (which fits some archetypes but not all of them). With a powerful enough culture, perhaps swayed by unhappiness, development of colony, strength of culture, etc and some other mechanic, one could peacefully convince a system to change empires.

The identity part would be more background stuff that influences and alters but doesn't really create broad sweeping changes. A small empire would have a weaker culture. An empire with many colors of spice among it's colonies would enjoy some benefit (happiness, prosperity, or relation options). An identity could be itself influenced with new colony buildings/tools. Drop enough military oriented happy tools on a lot of your colonies and you'll start being a police state.