Seven characters are open to being in a polyamorous relationship, which is indicated as "Dating (not exclusive)," in the player's relationship guide if a non-exclusive relationship has been selected. Dating relationships are determined by the player when the first pink heart is reached.
The characters who are open to non-exclusive relationships are:
Dating all of these characters simultaneously unlocks the Colony Charmer achievement. You cannot have a marriage ceremony or have a baby if you are in a polyamorous relationship. The developers were unable to overcome technical problems caused by allowing multiple move-in/marriage-level relationships (see https://steamcommunity.com/app/730050/discussions/0/1837937637889161573/)