@zeguy4uThere's a little of that in Celtic Bard's Justice Resurrected and in Sea-Life's Geeks in Space, but it's not a major plot point in either and everything is resolved easily.
Both two guys going for the same girl and two girls in competition for the same guy show up in Vincent Berg's Trying to be Normal but it all feels very tongue in cheek and gentle (well, for their part). It's fun, though โ my favorite subplot from the entire series.
IIRC, Wes Boyd's Dawnwalker was centered around a guy having to choose between three very different girls. But it wasn't a competition between them, it was him having figure out what he really wanted. Unfortunately, it doesn't look to be on SOL any longer.
From Hollywood, that was the plot for Death Becomes Her, and they were very mean to each other along the way.