I think it's not possible to go beyond 7, as far as I know there aren't accessories with two stars of the same color (but I'm still at level 18, so it's possible that I have still to unlock 'em).
Good thing I've got everything unlocked to this point. I can confirm there are no accessories that give you 2 stars in anything.
Right now, though, the highest point setups are:
Costume: 3VI (Idol@school EXT-07 or Change2MYColour EXT-08 or STA-15) 3DA (LUX-15) or 3 VO (EXT-09, FLO-15)
All these costumes are NOT DLC items, so you can get them in game sooner or later. There's also a 1DA, 2VO (EXT-03), and 1VI, 2VO (EXT-16)
Head: The crown is the best item, with 1/1/1 DA/VI/VO. Not DLC. (Hd-34)
Body: 1/1 pick any two stats. There's a lot of them. The DLC item is in fact just 1 star.
Hand: 1/1 pick any two stats. The DLC items (Both of them) are just 1 star.
Leg: 1/1 pick any two stats. The DLC item is 1 star.
So for absolute min/maxing:
You can get 7 stars in one catergory, 4 in the second, and 1 in the last.
If you're wondering on the item codes, they're the position they'd exist on the grid.
Now this is where things get fun.
I'm in the All star, and if you didn't know, you can adjust costumes in the idol setup.
More importantly:
With a 4 DA / 7 VI /1 VO setup with 3x 5 star lessons on a full level 35 team with Azusa, Takane and Miki, you will have stats of 462/644/468
When I direct Azusa (And only Azusa) to take off a 1VI/1DA item (The Ami & Mami Puppets in this case) we get 454/656/468
Now, remember, I have access to individual item equipment, so I can actually tell Azusa only to take off her accessory.
I now direct both Miki and Takane to take off their puppets. (Trio now don't have it) we get 448/650/468.
Now for extra credit...
I direct Takane to put her puppets back ON. We get 451/653/468.
So what is the takeaway here?
1. An equipment star seems to only be worth 14 points to an entire team. It's nice of course, but it should NOT break you.
2. If you do a partial equip on a trio, it's worth 8 points on the leader, and 3 points on each of the supports.
This would also imply that the formula for stats is 4/7 * leader + 2/7 for support idol 1 +2/7 for support idol 2.
I won't bother with the quintet calculations, but I imagine they're done with similar math, with the supports taking up a similar percentage.
Actually, now I REALLY think about it...
I suspect lessons are a % booster on your base stats, because I suspect I'm getting rounding errors. (14 is a weird number to stop at.)
Which in turn means that a star is always worth 10 in a stat, before a multiplier.
It would be easier to code across the board - each costume star is 10 points, and each grid star for each idol is 10 points.
Each lesson star increases the modifier on your stats by 0.1, with a base of 1.0 (So 5 stars will make the multiplier 1.5x)
I can't comment on the song modifier yet, only cause I want to get to sleep before an exam today. I'm sure someone else can do the test there. I don't think the song modifier is a multiple though (so 10 points per star), since it doesn't drastically affect your stats.
Edit from original post: Math changes. I got back to my desk from my living room, and corrected the math.
Edit 2: Thoughts before sitting a basic law exam.