Philolexian is not the only literary society to have existed at Columbia, though it's the only extant one.
*- In the early nineteenth century, the heyday of college literary societies, it was common for campuses to have two competing societies. Peithologian, founded in 1806 by College freshmen, who at the time were not allowed admission to Philolexian, grew to become Philo's counterpoint on the Columbia campus. Peithologian sputtered along into the twentieth century, suffering occasional periods of non-existence, before more or less ceasing to exist. In recent years feisty Philolexians occasionally ambitiously plan to splinter off and refound Peithologian, but rarely get around to actually doing it.
*- Contrary to what you might be led to believe, it had nothing to do with Barnard College. Founded in 1877 by dissident Philolexians who felt Philo wasn't serious enough, and obsequiously (hah!) named in honor of the then-president of the College, Frederick Augustus Porter Barnard, the BLA for about 30+ years was a serious debating force on the campus. It died out in the early twentieth century for reasons that are unclear to me.
*- Founded in 1893, the Hamilton Society existed for just over a month. Realizing that it was a good idea to infuse the lethargic Philolexian with new blood and vigor rather than let it die, the Hamilton Society was merged into Philo before the end of the school year, preserving Philo for another 60 years.
In April of 2005, the society adopted a Resolution to Claim the Legacies of the Peithologian Society and Barnard Literary Association, effectively placing their history under its guardianship.