Update 1: Thanks to Light Buster who says that all characters have a sleep over event.
Each character has a sleepover event.
When in Kirito mode you can get the sleep over events with these characters.
Get any of those characters to level 4 Affinity level and Upon talking to them a second time, your be given the "Go on a date" option, I've found choosing the middle of the three options has whats gotten the most sleep overs.
I've got a few of the others to level 4 and have not had anything come up for them.