An idea that I think has been mentioned before: I'd like to be able to create a single without moving to a second floor of rooms. My idea for this is to have any single dragged onto the player when there are no placed staffers get a 1 value for the missing elements. (Example: If you don't have a choreographer, then the player does that task at level 1.) A potential related side feature would be to allow dragging a single with finished elements back onto a staffer with better stats to replace the stat on the single. (As things are, you can simulate this by deleting the single and starting over.) The first part would help the early game move faster (or at least have more variety than constant photoshoots), while the second part can add to the complexity of strategies.
From a modding standpoint, I'd also be interested in having some of the traits of staffers be moddable. For instance, being able to change the gender of staffers or give them a different pair of skills. The player's influence skill probably has to remain hard-coded, but maybe the others can be mixed a bit. (It would also help with the composer, who is currently hard-coded to be male. Makes idols that become composers seem a bit odd, unless they are meant to be implied as crossdressers or transgender.)