The women claim Rubin and his associates lured them to New York on Jet Blue flights after contacting them on Instagram.
Once in Manhattan, they say he drugged them then violently beat them while they were gagged and bound in the sex dungeon, hitting woman so hard that she passed out as he demanded she call him 'daddy'.
His associates then gave them money to cover medical expenses incurred by the injuries he inflicted on them, they said.
He is named alongside associated Stephanie Shon, Jennifer Powers, and lawyer Yifat Schnur in the lawsuit.
Two of them say he warned them: 'I'm going to rape you like I rape my daughter,' before attacking them and one says he punched her breast so hard her implant 'flipped'.
They say he then covered up the alleged rapes and attacks and hushed them by paying them up to ,000 each.
Day hosted the November 5, 2011 episode of Saturday Night Live (SNL) with Maroon 5 as the musical guest.
He was the second cast member from It's Always Sunny in Philadelphia to host SNL (after Danny De Vito, though De Vito hosted SNL before It's Always Sunny in Philadelphia premiered).
In 2014, he received an honorary doctorate in performing arts from Merrimack, where he also delivered that year's keynote address.