There's considerable love for Bruce/Clark/Lois in fanfic as a way to resolve the opposing pulls of a popular Official Couple and a popular Ho Yay target, sometimes expanded to an OT4 of Bruce/Selina/Clark/Lois.
The crackier Clark/Lois/Metropolis. (Which is sort of canon, as Lois once commented that she's much more jealous of the city than of the scantily-clad superheroines Supes hangs out with.)
The Big Three, Clark/Bruce/Diana. In Mark Waid's The Kingdom miniseries, the Kingdom Come versions of Clark and Diana have a son with Bruce as the godfather — and the grown-up kid refers to them as his three parents. An AU featured in the 2008 Trinity series just had the three of them get married, basically.
Catwoman/Ivy/Harley (see especially Gotham City Sirens), Catwoman/Ivy/Batgirl (Barbara), Ivy/Harley/Batgirl, and Joker/Harley/Ivy (which is, at the very least, a canonical Love Triangle).
Riddler/Query/Echo in some groups. When you have two henchgirls who used to work in a fetish club, a villain who's more than once been hinted to be into that sort of thing, and the fact said henchgirls have gone to extremes to break him out… it's not exactly hard to connect some dots.
There are multiple potential Threesomes that revolve around the Barbara Gordon/Richard Grayson relationship. Starfire-Nightwing-Oracle covers the Love Triangle that revolves around Grayson, Oracle-Black Canary-Nightwing covers the Triangle that revolves around Gordon, and there are several other possibilities that involve various members of the Batfamily and Barbara's Birds of Prey team.
As well as a Starfire/Nightwing/Donna Troy threesome, to keep it in the Titans family, or a Barbara/Dick/Huntress threesome to keep it in the Birds of Prey
There are those who go for Green Arrow/Black Canary/Hal Jordan, as the former two are an on-and-off again Official Couple.
Harley Quinn is head over heels for the Joker but is heavily implied to have romances with her best friend Poison Ivy. Ivy/Harley shippers usually hate the Joker for being highly abusive, but some go for Joker/Harley/Ivy.
Cosmic Boy/Lightning Lad/Saturn Girl from Legion of Super-Heroes, given the closeness of the trio in canon. Ultra Boy/Apparition/Timber Wolf from the post-Zero Hour Legion isn't too beyond the pale, either.
From the cartoon, we have Superman/Brainiac 5/Kell-El.
Jason/Roy/Kori was part of what was the first wave of fanart for Red Hood and the Outlaws. After the title had ONLY been announced. And after issue one, in which Starfire has sex with Roy, and Jason states he'd "been with" her. In what might be a conscious rejection of the trope (and/or a retcon), Issue #6 reveals this to have been spending the entire night talking with her. Which hasn't stopped the fanart at all.
Stephanie Brown/Tim Drake/ Cassandra Cain used to be a fan favorite. The memory lives on in old fanfiction.
Kon/Tim/Cass exists for those who enjoy Kon/Tim, Kon/Cass, and Tim/Cass.
There's even some people that ship the Core Four of Young Justice, Bart/Tim/Conner/Cassie, together.
Really weirdly, the Watchmenfandom has taken a liking to Laurie/Dan/Rorschach. It would only be possible in an AU. Fandom has happily provided the AUs. Fits the "canon couple (Dan/Laurie) + subtexty partnership (Dan/Rorschach)" type.
