Well, the player COULD be in a position similar to the position taken in the Extra episode with RK; i.e., they are Reiko/Manami's assitant. In the case of Manami (who was the producer for both Ai and Ryo, though she focused more on Ai as Ryo was better at taking care of himself) the player might take over production responsibilities if she leaves as she did in DS. Another way this could work: add Cineria as an 876 idol and have either her or Eri be Reiko's idol, depending on which one the player's producing. (Neither leads to both...?) Manami could then be Mai's producer from the start.
Personally, I'm going with the "player is an assistant" theory. Maybe they/"we"(?) are an intern, like what Ritsuko was in the original games before she became an idol due to lack of idols. Plus, it would make for a cool "taking the reins" sorta plot thing. As for if you produce Eri instead... Perhaps Reiko leaves as Eri's producer once someone (coughcoughKuroicough) leaks that Eri's producer was a member of riola, mentioning the scandal. She would leave to prevent the rumor from ruining Eri's career as it had her own. (Or something...?) Now, as to why someone would want to leak something like that...
(Also, something kinda nitpicky: Manami is technically a manager, not a producer. Not sure what the difference is, but it's there.)