It is a rather fundamental change though - it moves conversation system from “avatar” speaking to party speaking and new systems would needed to be develop to support it both in single and multiplayer, alongside potential changes to the content of the conversations.
I think curent system would work well enough. O_o
First the game needs to check whos in our party ... wich i just realized it allready do.

Then you would need your companion specific dialogues ... question is if they allready are in same packet as regular options ... or if game would be abke to reach them in different packet ... or if they would need to be moved ...
Some work would be needed to explain the game that its supposed to take companions stats for dicerolls ...
There is question at hand: If our Tab is a Wizard ... and Gale is in party ... should we get only our [Wizard] taged option ... only the better stat option ... or both? I would say both.
But since our protagonist is silent ... and so are companions if they are talkers ... i dont think this would require any adjustments ...
Camera can still be focused on Tav as NPC react on whatever our companions said. It will return to us anyway.
Problem come with Multiplayer, bcs this way person who starts the conversation would be talking with as other ppl characters. :-/
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Potentialy expensive part come with passive checks ...
Since as our companions would suceed in those checks, they would need to tell us somehow.
Cheap, lazy solution would be to just let Narrator tell that *XY* shares his/her memory trough our connected minds ... and then just replay the same as when our character remembers.
But that would be weird, especialy in later parts as conpanions are against using tadpole.
So expensive solution would be record every companion saying those things out loud.
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Personaly i think the other system would be much better ...
//Edit:
That would just require to add option to click on conversating party ... and take over as a speaker, when you switch between your party members.
Big plus of such feature is that it can easily work in multiplayer aswell, it would only require adding single popup message, where speaker would need to confirm that he wants other player to lead conversation from now on.
Minor minus is that passive checks would still be rolled only by curently speaking character, just as they are now ... so its not too big loss.