At least when it comes to Shadowheart, the rule seems to be that blonde Shadowheart is open to it so long as it's not with other origin characters. She not only joins enthusiastically when offered to play with the twins but also has no problem with you getting with another individual who joins your camp. So this effectively means the only other companion you can be in a poly relationship with her with is Halsin, as neither Minsc nor Jaheira appear to be romance options and Minthara's romance arc seems to be nonexistent after Act 1.
I've also heard that Astarion is also able to enter into a poly romance involving Halsin, but have not confirmed it for myself.
The end result is that any stable companion poly romance must involve a male companion, something I personally find disappointing as I don't romance male characters in games.
The only options I could see for changing things would be to either, remove the bar on poly origin romances, make Jaheira a poly romance option, extend Minthara's romance, or add a new companion as a romance option. I don't see them doing the first, and while extending Minthara as a romance option is possible I think the only way to make it accessible to most players would be to add a way to save the grove and recruit her. Either Jaheira or a new companion would be relatively straight-forward, if a lot of work on Larian's part.
