I like the above mention of merch: Maybe you could pick an idol and create a photobook for her based off a stat, and then by combination of her fame/that stat level it affects the sales of the photobook/the amount of fans she gains from it?
An addition to theater I could see is being able to decide a setlist for performances: the quality of the song/its vocal and dance values might boost the training performers get. Also, I think idols need to be scheduled as well, and get boosts/stamina drain individually. I think it's a negative departure that the cafe has the ability to "schedule" girls (Sort of: If it's on manual, but you have to drag your girl back to the cafe if she finishes a shift which is already overly-tedious) but the theater doesn't when it could really be useful for boosting newer girls. We could pick 3 or so girls for each day, and they're the ones performing and getting boosts. Maybe not changing the setlist/performers over time might cause the audience to get bored and require you to switch it up over time and cycle songs/idols through the setlist, just to make the theater a bit more hands-on. I also think it'd be great if girls could gain some fans by being in the theater, and I think it kinda fits better into the idol growth cycle than gaining fans through waiting tables lol. And with the cap of a live audience being 300 and streaming having some barriers, I think it would avoid the runaway growth that the cafe gave girls.
Finally, with the addition of the new room type, this is something that's been bothering me: I think there's too much to look at. My building just SCRAWLS up and down the screen, out of sight. You have cafes and theaters which take up 2 floors with just one of each, two floors to fit break rooms and single production rooms, another two floors to fit doctors and offices: it's too much to keep track of now. I agree with a much earlier suggestion that it might be time to consider allowing the player to upgrade rooms, rather than forcing them to add another floor on top of what they have: An upgraded breakroom takes your old one and allows it to restore stamina for 10 idols at 1.25 the original cost, then 15, etc., the cafe has its capacity doubled when upgraded, the office upgrade allows more than one staffer to work there.... The dollhouse style looks nice when you're only utilizing the first two or three floors with only a few roomtypes, but as the complexity goes up, it gets messy (Especially when you have to process things like business deals when your worker is 3 stories apart from the other two.) The released singles also could use some de-cluttering, like with separating sister group singles.