Feathered Nests features an alien race where polyamory is the norm, and it spills over onto humans.
In Frankenstein's Family, Dénes and Dorottya are a couple. Csilla the vampire is a more recent addition, connected by them feeding her, the resultant empathic ties, and erotic spillover. Not really the usual sort of triad, but definitely a poly relationship.
The Godship Wanderers has a triad, and actually most of the refugees have banded into small groups. Bembé is a bisexual man, Homero is gay, and Lur is a heterosexual woman.
Hart's Farm is very nearly a polyvillage. They're more given to loose conglomerations of favorites than to permanent grouplets.
The Ocracies has some nations that run to poly relationships, as mentioned in "It Takes Three."
The Odd Trio has Druga, a dwarven woman; Elan, an elven man; and Hope, an asexual human man.
Polychrome Heroics has a lot. In Antimatter & Stalwart Stan, Hefty and Fiddlesticks are partners, Fiddlesticks and Diamond are married, Hefty and Roger are married, Roger and Diamond are increasingly close friends. So it's a foursquare made of several different types of tie. Aquariana's thread is set in the Republic of the Maldives, a Muslim nation, where polygamy is considered normal. Cassandra's thread has Highliner, Bryony, and Yona who are married with children. In Cuoio and Chiara, those two are boss and comare, but Salvo is nearly as close, and Cuoio is very attached to everyone on his team. In Officer Pink, Ansel and Janie have a romantic relationship, and Turq has pretty much crept in as a platonic third. Ruggiero, Olympia, and Liborio are a triad because the latter two have interests that really don't appeal to their vanilla-gelato boss. The Parquetry family is introduced in "A River So Long."
I'm not on Tumblr, so I can't post things there. But if anyone wants to post my recent poly writing on Polyshipping Day, go for it. Linkluv is awesome. :D Also, feel free to request poly anything during prompt calls.