Some random math to figure some things out. Mostly ages and relative years.

Mai is 29 years old

Kotori is ≤25 years old

Arcade is at year 0 for these purposes, as is 360 and SP(each as a seperate storyline).

DS, and iM@S 2 are year 1.

I'm not sure how long after 360 L4U is set, so that's not included. (Not like it matters anyway, being just a stage show game with little to no plot attached...)

In DS, Mai is 29. If she was 16 during her idol days, that makes a 13 year gap, putting the game at a potential year -12(Or, twelve years before the events of any of the games, thirteen before 2.)

In the original games, Kotori is ≤25. Taking at her highest possible age, 25, the oldest she can be is 13. (loli!Kotori? It's not really that unlikely an age... I mean, look at Yayoi, Ai, and the Futami's!)

An even middle number for this puts the third mystery idol(the one who fell in love with Takagi... in theory) would be 14 or 15. If she would be older than the other two, then 18 would also work. That'd make her, at the oldest, 30 as of year 0. (Unless she debuted at somewhere like Azusa's age, where she'd be older...)

If playing as Takagi for the purposes of the game, that'd make him 42 as of year 0. (That seems a bit old to me...)

Also, image colors: We know Kotori's would be the "light yellow color of chicks", but what would Mai's be? Some form of red or scarlet? That would leave a blue or greenish color to the third idol...