Rock Bands can fight other Rock Bands somehow, maybe they have to have a special promotion or there is a promotion that makes them better at it. This might require a whole 3rd type of combat, making it really complicated. It might be easier to just have Rock Bands with a certain promotion (Folk/Country Band?) mitigate the impact of foreign bands in a city's territory if you park them there.

Have specific genres available. Rap/hip-hop units generate more culture per turn (most popular genre right now) and they have a drive-by promotion where they can kill other units.

JK but the thought of naming my band Tupac and sending him out to kill other bands in between tours is hilarious.