I really enjoy this game and I haven't stopped playing since i bought it, but I think these would make it more interesting:
Sometimes when members are being bullied, they should expose the member on sns - but also sometimes bullies should falsely accuse their victim. It should then be up to you to decide how to handle the situation and possibly receive scandal points depending on your choice.
To be able to rename groups and disband them.
B-side songs, graduation singles, graduation concerts & albums.
A bootcamp feature where you can send an idol for different periods of time and they receive boosts in their skills depending on how long they're sent for - however their stamina is greatly reduced during this time.
Sub-units, duos & solo's.
Higher capacity of members for songs.
Feedback from fans (or anti's) on sns about various things - such as cute/pretty/cool/sexy skill, vocal skill, dance skill, intelligence, funniness, charisma, backlash from male fans who attend a handshake event and interact with an idol with misandry, an idol not being included/always in back row/always being center/etc.
Ballad as a song type, graduation song as a marketing point & graduation lyrics.
Idols rejoining after graduation sometimes.
More variety in scandals.
Scandal points for putting members under 18 in bikini singles or songs with sexy choreo.
Idols themselves choosing to go onto hiatus for reasons like school/mental health/exhaustion.
Criticism if lots of your idols have low skills.
Having a kenkyuusei system similar to AKB48's.
TV show, photoshoots, variety show & advertisement deals sometimes being for multiple members.
EDIT: Oh and I forgot to say international members and possibly international auditions.