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The ability to initiate conversations using a companion leads to characterisation issues.

Am I playing as the PC and interacting with independent companions or am I in full control of a party of adventurers ?

On the one hand, you have created companions with their own personalities. Sometimes my PC will be forced to talk to them, sometimes they will interject in a conversation that my PC initiated with an NPC, sometimes they approve/disapprove of what my PC says. So they are established as their own individuals. Pretty clear.

On the other hand, if I initiate a conversation using a companion, I can have them select lines that are completely out of character (like Wyll approving of Kagha, Lae'zel licking Crusher's foot, etc).

That hurts immersion.

I really agree with this one, so much so that I'm thinking of making an independent thread for it. Companions are autonomous characters in the world with their own opinions and motivation, it makes no sense that I would get limited control of their dialogue options to contradict their preestablished characterisation. Especially since sometimes I just happen to have a random companion selected when a dialogue initiates, and I have no way of changing it without going back.

I remember I had shadowheart selected when I initiated the lae'zel recruitment dialogue when she's in the cage. I wanted to recruit lae'zel and save her, but its clear that shadowheart doesn't want that. But because she happens to lead the conversation, I had to express my decisions through her character instead of my own where it makes sense, which broke immersion when she hates lae'zel immediately after.

Honestly the solution for me is simple, don't allow us to lead conversation as companion characters. Always have it be the player character, and add a mechanic where party members can intervene either autonomously or through hand selected dialogue options specific for their character (that doesn't allow for blatant contradictions).

I don't understand the rationale of this mechanic, its not like a dungeon master would allow you to roleplay the entire supporting cast of your campaign. You should only really be able to roleplay your character, and have companions intervene for either skill checks or character specific dialogue when it makes sense.