How do you handle your partner's break-up with another partner?
Support without inserting yourself. The break-up is theirs to grieve; your role is to be present, attend to their wellbeing, and not treat the loss as a structural improvement for your own relationship. Show up for the grief; don't editorialise on the metamour.
When your partner breaks up with another partner, you are in a particular position: close enough to the situation to feel it, far enough from it that the loss is theirs and not yours. The skill is being supportive without inserting yourself into the grief that belongs to the other relationship.
What helps. Show up for the grief practically and emotionally — make sure they're eating and sleeping in the rough weeks, offer presence without forcing closeness, ask what kind of support they want rather than assuming. Honour the relationship that ended without overstating your own role. Acknowledge the metamour as a real loss for your partner, even if you weren't close to the metamour yourself.
What does not help. Treating the break-up as a quiet relief for your own relationship ('great, more of their time for me now'). Editorialising on the metamour after the fact ('I always thought they were'). Pushing for immediate reorganisation of time and attention as if the freed-up bandwidth is now yours. Expecting your partner to grieve faster than they actually need to.
If you had a polyaffective relationship with the metamour. That bond does not necessarily have to end just because the romantic relationship between them and your partner ended. Some metamour friendships persist past the romantic break-up; some don't; both outcomes are reasonable. The decision about whether to continue your relationship with the metamour is yours and theirs, separately from the romantic relationship that ended.
If the break-up was bad. If the ending involved conflict, harm, or genuine wrong, your partner may have feelings about the metamour that are sharper than mere grief. Don't pile on; don't excuse; do listen. Help them get to whatever clarity they need without trying to control the shape of that clarity.