A few random things that might be fun:
1) Adding an international trait (based on your Ma Rio name post on Twitter), where having an international girl in your lineup will increase revenue on an international tour.
2) Implementing some sort of task list/tutorial at the beginning to try and ensure that the company remains solvent until the first single or two is released.
3) Being able to save certain formations/lineups so you don't have to drag and drop 15 girls every time you release a single.
4) Having the ability to produce "subgroups" and other groups under the same label.
5) Having something like a mixi ranking, that is an unofficial (partially randomly generated, partially based on who has the highest fame/who has been pushed/who has been center/who has gotten promotions recently) ranking of the girl's popularity outside of the yearly election event.
5a) This could affect the sales of singles. For example, the AKB48 janken singles often sold less because the senbatsu were not center--so the diehard fans might not purchase as many singles if the girls that they like aren't center.
5b) Certain girls might have different popularity rankings with different fans. For instance, Girl A might appeal more to casual fans, whereas Girl B might appeal more to diehard fans. The lineup of singles might affect the sales as well.