John Mulaney's character, Simon Sawyer, is based on "Company" composer Stephen Sondheim, and Paula Pell's character, Patty, is based on actress Elaine Stritch.
Parody of the documentary Original Cast Album: Company.
Richard Kind's song "Christmas Tips" contains a reference to an SNL piece John Mulaney wrote for Stefon, a character portrayed by Bill Hader on Weekend Update: that being a doorman who only gives high fives to children of divorce.
Alex Brightman (Kenny) has some experience with the episode's premise; his first Broadway acting job was working as an understudy in 2008's "Glory Days", which closed after just one regular (non-preview) performance. Brightman never got the chance to be onstage for the show; he would make his Broadway debut later that year as Boq in 'Wicked".
Though most elements in this episode parody the musical Company and the D. A. Pennebaker documentary about the recording of its cast album, the revelation early in the episode that the show Co-Op has closed before the album can be recorded is drawn from another Stephen Sondheim / Hal Prince collaboration, the 1981 musical Merrily We Roll Along. Unlike Company, which was a huge hit and won multiple Tonys, Merrily ran for 52 troubled preview performances and only 19 regular performances, and the cast had to record the original cast album the day after the show closed.