Basically, it depends on the type of polyamorous type relationship you are having.
If you are having a relationship where person a is dating person b and c, but b and c aren't dating, then it's very similar to a monogamous breakup expept person a will still be dating one of the people.
If it's a throuple relationship where all 3 people are dating each other, it might become a relationship like the one mentioned in the start of my first example with a dating b and c but c and c no longer dating.
It's also possible that they might be broken up with multiple partners if they are in a closed polygamous style of relationship where they aren't allowed to date someone outside their group and have a rule were everyone must date each other… but this form of plyamory is a lot more rare.