Side games should be:
Kairi/Riku/Mickey search for way to bring Sora back
Terra/Aqua/Ven investigate the black box
Roxas/Axel/Xion delve into the data-worlds to access lost Ansem The Wise data about Girl X
In each game, you can swap between the characters and it's treated more like a RPG with more detail on characters' unique abilities to help differentiate them. Namine serves as the journal keeper and also a telepathic link between the three groups.
Certainly a neat idea.
The first group could also hopefully get into contact with the TWEWY-gang and finally give Kairi some interactions and bonding with characters that aren't Sora. Especially Riku comes to mind but her interacting with Neku & co. or the King would also be a neat concept.
The second group could have also several things going on beside just the black box alone considering that during the ending Ventus got his Chirithy back and Lauriam, Elrena, Luxord and Demyx are implied to return as full people eventually and they are tied to the mysteries of that era just like Ven.
Regarding Ven's memories of the distant past it is also a possibility that the Wayfinder Group will have to turn to Naminé directly if she retains her memory powers.
The third group would obviously also include Isa as he was the one to bring up the whole Subject X subplot in the first place. Needless to say that if Subject X turns out to be Skuld after all the road of the Twilight Group will eventually converge with the one of the Wayfinder Group.
As AdrianXXII says, for connection and information exchange between the three partys certainly the gummi phone would be used as the part where Jiminy states they prepared one for everyone in Team Light wasn't there for nothing, but Naminé taking the role of mission control and bringing together the information and results from every party would still be a neat way to include her.
I also bet she would do things a dozen times better than Yen Sid.
The question where Naminé sets up her "command post" could also be an interesting endeavour considering who she could have for assistance and possibly further interactions to boost her self-worth more.
If she resides in Twilight Town, she could have HPO + possibly Scrooge and Cifer's gang for assistance, in Disney Castle she could have Chip & Dale, Minnie and Daisy while at Radiant Garden she could have Leon & the gang if they finally decide to bring them back + Ienzo and the other apprentices.